diff --git a/compiler/rustc_middle/src/ty/flags.rs b/compiler/rustc_middle/src/ty/flags.rs
index ea6bb8a7abd..49db121db1b 100644
--- a/compiler/rustc_middle/src/ty/flags.rs
+++ b/compiler/rustc_middle/src/ty/flags.rs
@@ -207,6 +207,11 @@ impl FlagComputation {
 
             &ty::FnDef(_, substs) => {
                 self.add_substs(substs);
+                // HACK(#98608, oli-obk): Function items with opaque types in their signature will
+                // end up not having the HAS_TY_OPAQUE flag set, causing `evaluate_obligation` to
+                // optimistically assume the function item matches any signature. See documentation
+                // on `HAS_FREE_LOCAL_NAMES` for details.
+                self.add_flags(TypeFlags::HAS_TY_OPAQUE);
             }
 
             &ty::FnPtr(fn_sig) => self.bound_computation(fn_sig, |computation, fn_sig| {
diff --git a/src/test/ui/type-alias-impl-trait/issue-53398-cyclic-types.rs b/src/test/ui/type-alias-impl-trait/issue-53398-cyclic-types.rs
index 6c838f41003..4bc0f9d9200 100644
--- a/src/test/ui/type-alias-impl-trait/issue-53398-cyclic-types.rs
+++ b/src/test/ui/type-alias-impl-trait/issue-53398-cyclic-types.rs
@@ -3,7 +3,7 @@
 type Foo = impl Fn() -> Foo;
 
 fn foo() -> Foo {
-    foo //~ ERROR: overflow evaluating the requirement `fn() -> Foo {foo}: Sized`
+    foo //~ ERROR: overflow evaluating the requirement `<fn() -> Foo {foo} as FnOnce<()>>::Output == fn() -> Foo {foo}`
 }
 
 fn main() {}
diff --git a/src/test/ui/type-alias-impl-trait/issue-53398-cyclic-types.stderr b/src/test/ui/type-alias-impl-trait/issue-53398-cyclic-types.stderr
index a9c2c18630c..f69514b7808 100644
--- a/src/test/ui/type-alias-impl-trait/issue-53398-cyclic-types.stderr
+++ b/src/test/ui/type-alias-impl-trait/issue-53398-cyclic-types.stderr
@@ -1,10 +1,8 @@
-error[E0275]: overflow evaluating the requirement `fn() -> Foo {foo}: Sized`
+error[E0275]: overflow evaluating the requirement `<fn() -> Foo {foo} as FnOnce<()>>::Output == fn() -> Foo {foo}`
   --> $DIR/issue-53398-cyclic-types.rs:6:5
    |
 LL |     foo
    |     ^^^
-   |
-   = help: consider increasing the recursion limit by adding a `#![recursion_limit = "256"]` attribute to your crate (`issue_53398_cyclic_types`)
 
 error: aborting due to previous error
 
diff --git a/src/test/ui/type-alias-impl-trait/issue-98604.rs b/src/test/ui/type-alias-impl-trait/issue-98604.rs
new file mode 100644
index 00000000000..a4fd8a82a04
--- /dev/null
+++ b/src/test/ui/type-alias-impl-trait/issue-98604.rs
@@ -0,0 +1,13 @@
+// edition:2018
+
+type AsyncFnPtr = Box<
+    dyn Fn() -> std::pin::Pin<Box<dyn std::future::Future<Output = ()>>>,
+>;
+
+async fn test() {}
+
+#[allow(unused_must_use)]
+fn main() {
+    Box::new(test) as AsyncFnPtr;
+    //~^ ERROR type mismatch
+}
diff --git a/src/test/ui/type-alias-impl-trait/issue-98604.stderr b/src/test/ui/type-alias-impl-trait/issue-98604.stderr
new file mode 100644
index 00000000000..f04d1b4d787
--- /dev/null
+++ b/src/test/ui/type-alias-impl-trait/issue-98604.stderr
@@ -0,0 +1,18 @@
+error[E0271]: type mismatch resolving `<fn() -> impl Future<Output = ()> {test} as FnOnce<()>>::Output == Pin<Box<(dyn Future<Output = ()> + 'static)>>`
+  --> $DIR/issue-98604.rs:11:5
+   |
+LL |     Box::new(test) as AsyncFnPtr;
+   |     ^^^^^^^^^^^^^^ expected struct `Pin`, found opaque type
+   |
+note: while checking the return type of the `async fn`
+  --> $DIR/issue-98604.rs:7:17
+   |
+LL | async fn test() {}
+   |                 ^ checked the `Output` of this `async fn`, found opaque type
+   = note:   expected struct `Pin<Box<(dyn Future<Output = ()> + 'static)>>`
+           found opaque type `impl Future<Output = ()>`
+   = note: required for the cast from `fn() -> impl Future<Output = ()> {test}` to the object type `dyn Fn() -> Pin<Box<(dyn Future<Output = ()> + 'static)>>`
+
+error: aborting due to previous error
+
+For more information about this error, try `rustc --explain E0271`.
diff --git a/src/test/ui/type-alias-impl-trait/issue-98608.rs b/src/test/ui/type-alias-impl-trait/issue-98608.rs
new file mode 100644
index 00000000000..d75762a8b62
--- /dev/null
+++ b/src/test/ui/type-alias-impl-trait/issue-98608.rs
@@ -0,0 +1,9 @@
+fn hi() -> impl Sized { std::ptr::null::<u8>() }
+
+fn main() {
+    let b: Box<dyn Fn() -> Box<u8>> = Box::new(hi);
+    //~^ ERROR type mismatch resolving `<fn() -> impl Sized {hi} as FnOnce<()>>::Output == Box<u8>`
+    let boxed = b();
+    let null = *boxed;
+    println!("{null:?}");
+}
diff --git a/src/test/ui/type-alias-impl-trait/issue-98608.stderr b/src/test/ui/type-alias-impl-trait/issue-98608.stderr
new file mode 100644
index 00000000000..8f3ec7d9d16
--- /dev/null
+++ b/src/test/ui/type-alias-impl-trait/issue-98608.stderr
@@ -0,0 +1,16 @@
+error[E0271]: type mismatch resolving `<fn() -> impl Sized {hi} as FnOnce<()>>::Output == Box<u8>`
+  --> $DIR/issue-98608.rs:4:39
+   |
+LL | fn hi() -> impl Sized { std::ptr::null::<u8>() }
+   |            ---------- the found opaque type
+...
+LL |     let b: Box<dyn Fn() -> Box<u8>> = Box::new(hi);
+   |                                       ^^^^^^^^^^^^ expected struct `Box`, found opaque type
+   |
+   = note:   expected struct `Box<u8>`
+           found opaque type `impl Sized`
+   = note: required for the cast from `fn() -> impl Sized {hi}` to the object type `dyn Fn() -> Box<u8>`
+
+error: aborting due to previous error
+
+For more information about this error, try `rustc --explain E0271`.