diff --git a/compiler/fir/fir2ir/src/org/jetbrains/kotlin/fir/backend/Fir2IrClassifierStorage.kt b/compiler/fir/fir2ir/src/org/jetbrains/kotlin/fir/backend/Fir2IrClassifierStorage.kt
index 8af86172191..a8b0ceaf0e2 100644
--- a/compiler/fir/fir2ir/src/org/jetbrains/kotlin/fir/backend/Fir2IrClassifierStorage.kt
+++ b/compiler/fir/fir2ir/src/org/jetbrains/kotlin/fir/backend/Fir2IrClassifierStorage.kt
@@ -29,7 +29,8 @@ import org.jetbrains.kotlin.name.SpecialNames
 
 class Fir2IrClassifierStorage(
     private val components: Fir2IrComponents,
-    commonMemberStorage: Fir2IrCommonMemberStorage
+    commonMemberStorage: Fir2IrCommonMemberStorage,
+    private val conversionScope: Fir2IrConversionScope,
 ) : Fir2IrComponents by components {
     private val classCache: MutableMap<FirRegularClass, IrClass> = commonMemberStorage.classCache
 
@@ -287,19 +288,26 @@ class Fir2IrClassifierStorage(
         // Before the call it's not possible, because f/o binding for regular classes isn't done yet
         processMembersOfClassesOnTheFlyImmediately = true
         for ((klass, irClass) in localClassesCreatedOnTheFly) {
-            converter.processClassMembers(klass, irClass)
-            // See the problem from KT-57441
-//            class Wrapper {
-//                private val dummy = object: Bar {}
-//                private val bar = object: Bar by dummy {}
-//            }
-//            interface Bar {
-//                val foo: String
-//                    get() = ""
-//            }
-            // When we are building bar.foo fake override, we should call dummy.foo,
-            // so we should have object : Bar.foo fake override to be built and bound.
-            converter.bindFakeOverridesInClass(irClass)
+            conversionScope.withContainingFirClass(klass) {
+                classifiersGenerator.processClassHeader(klass, irClass)
+                converter.processClassMembers(klass, irClass)
+                // See the problem from KT-57441
+                //
+                // ```kt
+                // class Wrapper {
+                //     private val dummy = object: Bar {}
+                //     private val bar = object: Bar by dummy {}
+                // }
+                // interface Bar {
+                //     val foo: String
+                //         get() = ""
+                // }
+                // ```
+                //
+                // When we are building bar.foo fake override, we should call dummy.foo,
+                // so we should have object : Bar.foo fake override to be built and bound.
+                converter.bindFakeOverridesInClass(irClass)
+            }
         }
         localClassesCreatedOnTheFly.clear()
     }
diff --git a/compiler/fir/fir2ir/src/org/jetbrains/kotlin/fir/backend/Fir2IrComponentsStorage.kt b/compiler/fir/fir2ir/src/org/jetbrains/kotlin/fir/backend/Fir2IrComponentsStorage.kt
index c3e3f5bdade..dfa04139831 100644
--- a/compiler/fir/fir2ir/src/org/jetbrains/kotlin/fir/backend/Fir2IrComponentsStorage.kt
+++ b/compiler/fir/fir2ir/src/org/jetbrains/kotlin/fir/backend/Fir2IrComponentsStorage.kt
@@ -40,9 +40,11 @@ class Fir2IrComponentsStorage(
     override val signatureComposer: FirBasedSignatureComposer = commonMemberStorage.firSignatureComposer
     override val symbolTable: SymbolTable = commonMemberStorage.symbolTable
 
-    override val converter: Fir2IrConverter = Fir2IrConverter(moduleDescriptor, this)
+    private val conversionScope = Fir2IrConversionScope(configuration)
 
-    override val classifierStorage: Fir2IrClassifierStorage = Fir2IrClassifierStorage(this, commonMemberStorage)
+    override val converter: Fir2IrConverter = Fir2IrConverter(moduleDescriptor, this, conversionScope)
+
+    override val classifierStorage: Fir2IrClassifierStorage = Fir2IrClassifierStorage(this, commonMemberStorage, conversionScope)
     override val declarationStorage: Fir2IrDeclarationStorage = Fir2IrDeclarationStorage(this, moduleDescriptor, commonMemberStorage)
 
     override val callablesGenerator: Fir2IrCallableDeclarationsGenerator = Fir2IrCallableDeclarationsGenerator(this)
@@ -59,7 +61,6 @@ class Fir2IrComponentsStorage(
     override val irProviders: List<IrProvider> = listOf(FirIrProvider(this))
 
     override val typeConverter: Fir2IrTypeConverter = Fir2IrTypeConverter(this)
-    private val conversionScope = Fir2IrConversionScope(configuration)
 
     val fir2IrVisitor: Fir2IrVisitor = Fir2IrVisitor(this, conversionScope)
 
diff --git a/compiler/fir/fir2ir/src/org/jetbrains/kotlin/fir/backend/Fir2IrConversionScope.kt b/compiler/fir/fir2ir/src/org/jetbrains/kotlin/fir/backend/Fir2IrConversionScope.kt
index 7f8aa8f9f7d..7686d7a5e9c 100644
--- a/compiler/fir/fir2ir/src/org/jetbrains/kotlin/fir/backend/Fir2IrConversionScope.kt
+++ b/compiler/fir/fir2ir/src/org/jetbrains/kotlin/fir/backend/Fir2IrConversionScope.kt
@@ -5,10 +5,7 @@
 
 package org.jetbrains.kotlin.fir.backend
 
-import org.jetbrains.kotlin.fir.declarations.FirClass
-import org.jetbrains.kotlin.fir.declarations.FirConstructor
-import org.jetbrains.kotlin.fir.declarations.FirProperty
-import org.jetbrains.kotlin.fir.declarations.FirPropertyAccessor
+import org.jetbrains.kotlin.fir.declarations.*
 import org.jetbrains.kotlin.fir.expressions.FirReturnExpression
 import org.jetbrains.kotlin.ir.builders.Scope
 import org.jetbrains.kotlin.ir.declarations.*
diff --git a/compiler/fir/fir2ir/src/org/jetbrains/kotlin/fir/backend/Fir2IrConverter.kt b/compiler/fir/fir2ir/src/org/jetbrains/kotlin/fir/backend/Fir2IrConverter.kt
index 8e1606e04bc..f757c565ab3 100644
--- a/compiler/fir/fir2ir/src/org/jetbrains/kotlin/fir/backend/Fir2IrConverter.kt
+++ b/compiler/fir/fir2ir/src/org/jetbrains/kotlin/fir/backend/Fir2IrConverter.kt
@@ -61,7 +61,8 @@ import org.jetbrains.kotlin.psi.KtFile
 
 class Fir2IrConverter(
     private val moduleDescriptor: FirModuleDescriptor,
-    private val components: Fir2IrComponents
+    private val components: Fir2IrComponents,
+    private val conversionScope: Fir2IrConversionScope,
 ) : Fir2IrComponents by components {
 
     private val generatorExtensions = session.extensionService.declarationGenerators
@@ -137,15 +138,19 @@ class Fir2IrConverter(
 
     fun processLocalClassAndNestedClassesOnTheFly(klass: FirClass, parent: IrDeclarationParent): IrClass {
         val irClass = registerClassAndNestedClasses(klass, parent)
-        processClassAndNestedClassHeaders(klass)
+        conversionScope.withContainingFirClass(klass) {
+            processClassAndNestedClassHeaders(klass)
+        }
         return irClass
     }
 
     fun processLocalClassAndNestedClasses(klass: FirClass, parent: IrDeclarationParent): IrClass {
         val irClass = registerClassAndNestedClasses(klass, parent)
-        processClassAndNestedClassHeaders(klass)
-        processClassMembers(klass, irClass)
-        bindFakeOverridesInClass(irClass)
+        conversionScope.withContainingFirClass(klass) {
+            processClassAndNestedClassHeaders(klass)
+            processClassMembers(klass, irClass)
+            bindFakeOverridesInClass(irClass)
+        }
         return irClass
     }