diff --git a/compiler/src/dotty/tools/dotc/transform/SpecializeFunctions.scala b/compiler/src/dotty/tools/dotc/transform/SpecializeFunctions.scala
index 094d6024eb4e..43aef6279cec 100644
--- a/compiler/src/dotty/tools/dotc/transform/SpecializeFunctions.scala
+++ b/compiler/src/dotty/tools/dotc/transform/SpecializeFunctions.scala
@@ -3,7 +3,7 @@ package transform
 
 import ast.Trees.*, ast.tpd, core.*
 import Contexts.*, Types.*, Decorators.*, Symbols.*, DenotTransformers.*
-import SymDenotations.*, Scopes.*, StdNames.*, NameOps.*, Names.*
+import SymDenotations.*, Scopes.*, StdNames.*, NameOps.*, Names.*, NameKinds.*
 import MegaPhase.MiniPhase
 
 
@@ -25,7 +25,24 @@ class SpecializeFunctions extends MiniPhase {
   /** Create forwarders from the generic applys to the specialized ones.
    */
   override def transformDefDef(ddef: DefDef)(using Context) = {
-    if ddef.name != nme.apply
+    // Note on special case for inline `apply`s:
+    //   `apply` and `apply$retainedBody` are specialized in this transformation.
+    //   `apply$retainedBody` have the name kind `BodyRetainerName`, these contain
+    //   the runtime implementation of an inline `apply` that implements (or overrides)
+    //   the `FunctionN.apply` method. The inline method is not specialized, it will
+    //   be replaced with the implementation of `apply$retainedBody`. The following code
+    //      inline def apply(x: Int): Double = x.toDouble:Double
+    //      private def apply$retainedBody(x: Int): Double = x.toDouble:Double
+    //   in is transformed into
+    //      inline def apply(x: Int): Double = x.toDouble:Double
+    //      private def apply$retainedBody(x: Int): Double = this.apply$mcDI$sp(x)
+    //      def apply$mcDI$sp(v: Int): Double = x.toDouble:Double
+    //   after erasure it will become
+    //      def apply(v: Int): Double = this.apply$mcDI$sp(v) // from apply$retainedBody
+    //      def apply$mcDI$sp(v: Int): Double = v.toDouble():Double
+    //      def apply(v1: Object): Object = Double.box(this.apply(Int.unbox(v1))) // erasure bridge
+
+    if ddef.name.asTermName.exclude(BodyRetainerName) != nme.apply
        || ddef.termParamss.length != 1
        || ddef.termParamss.head.length > 2
        || !ctx.owner.isClass
@@ -44,12 +61,12 @@ class SpecializeFunctions extends MiniPhase {
       defn.isSpecializableFunction(cls, paramTypes, retType)
     }
 
-    if (sym.is(Flags.Deferred) || !isSpecializable) return ddef
+    if (sym.is(Flags.Deferred) || sym.is(Flags.Inline) || !isSpecializable) return ddef
 
     val specializedApply = newSymbol(
         cls,
         specName.nn,
-        sym.flags | Flags.Synthetic,
+        (sym.flags | Flags.Synthetic) &~ Flags.Private, // Private flag can be set if the name is a BodyRetainerName
         sym.info
       ).entered
 
diff --git a/tests/pos/i19724.scala b/tests/pos/i19724.scala
new file mode 100644
index 000000000000..776cf9167890
--- /dev/null
+++ b/tests/pos/i19724.scala
@@ -0,0 +1,5 @@
+object repro:
+  abstract class Mapper[A, B] extends (A => B)
+
+  given Mapper[Int, Double] with
+    inline def apply(v: Int): Double = v.toDouble
diff --git a/tests/run/i19724.scala b/tests/run/i19724.scala
new file mode 100644
index 000000000000..0ed6fcb94c57
--- /dev/null
+++ b/tests/run/i19724.scala
@@ -0,0 +1,18 @@
+class F0 extends (() => Double):
+  inline def apply(): Double = 1.toDouble
+
+class F1 extends (Int => Double):
+  inline def apply(v: Int): Double = v.toDouble
+
+class F2 extends ((Int, Int) => Double):
+  inline def apply(v1: Int, v2: Int): Double = (v1 + v2).toDouble
+
+@main def Test =
+  val f0: (() => Double) = new F0
+  assert(f0() == 1.0)
+
+  val f1: (Int => Double) = new F1
+  assert(f1(3) == 3.0)
+
+  val f2: ((Int, Int) => Double) = new F2
+  assert(f2(3, 2) == 5.0)