diff --git a/compiler/rustc_hir_typeck/src/method/suggest.rs b/compiler/rustc_hir_typeck/src/method/suggest.rs
index eaf40a193a6..cb20a1d7c7b 100644
--- a/compiler/rustc_hir_typeck/src/method/suggest.rs
+++ b/compiler/rustc_hir_typeck/src/method/suggest.rs
@@ -100,9 +100,9 @@ fn impl_into_iterator_should_be_iterator(
         ty: Ty<'tcx>,
         span: Span,
         unsatisfied_predicates: &Vec<(
-            ty::Predicate<'_>,
-            Option<ty::Predicate<'_>>,
-            Option<ObligationCause<'_>>,
+            ty::Predicate<'tcx>,
+            Option<ty::Predicate<'tcx>>,
+            Option<ObligationCause<'tcx>>,
         )>,
     ) -> bool {
         fn predicate_bounds_generic_param<'tcx>(
@@ -131,15 +131,17 @@ fn predicate_bounds_generic_param<'tcx>(
             }
         }
 
-        fn is_iterator_predicate(predicate: ty::Predicate<'_>, tcx: TyCtxt<'_>) -> bool {
+        let is_iterator_predicate = |predicate: ty::Predicate<'tcx>| -> bool {
             if let ty::PredicateKind::Clause(ty::ClauseKind::Trait(trait_pred)) =
                 predicate.kind().as_ref().skip_binder()
             {
-                tcx.is_diagnostic_item(sym::Iterator, trait_pred.trait_ref.def_id)
+                self.tcx.is_diagnostic_item(sym::Iterator, trait_pred.trait_ref.def_id)
+                    // ignore unsatisfied predicates generated from trying to auto-ref ty (#127511)
+                    && trait_pred.trait_ref.self_ty() == ty
             } else {
                 false
             }
-        }
+        };
 
         // Does the `ty` implement `IntoIterator`?
         let Some(into_iterator_trait) = self.tcx.get_diagnostic_item(sym::IntoIterator) else {
@@ -164,7 +166,7 @@ fn is_iterator_predicate(predicate: ty::Predicate<'_>, tcx: TyCtxt<'_>) -> bool
                         generics,
                         generic_param,
                         self.tcx,
-                    ) && is_iterator_predicate(unsatisfied.0, self.tcx)
+                    ) && is_iterator_predicate(unsatisfied.0)
                     {
                         return true;
                     }
@@ -172,7 +174,7 @@ fn is_iterator_predicate(predicate: ty::Predicate<'_>, tcx: TyCtxt<'_>) -> bool
             }
             ty::Slice(..) | ty::Adt(..) | ty::Alias(ty::Opaque, _) => {
                 for unsatisfied in unsatisfied_predicates.iter() {
-                    if is_iterator_predicate(unsatisfied.0, self.tcx) {
+                    if is_iterator_predicate(unsatisfied.0) {
                         return true;
                     }
                 }
diff --git a/tests/ui/iterators/iterator-does-not-need-into-iter.rs b/tests/ui/iterators/iterator-does-not-need-into-iter.rs
new file mode 100644
index 00000000000..29196449e30
--- /dev/null
+++ b/tests/ui/iterators/iterator-does-not-need-into-iter.rs
@@ -0,0 +1,18 @@
+//! regression test for #127511: don't suggest `.into_iter()` on iterators
+
+trait Missing {}
+trait HasMethod {
+    fn foo(self);
+}
+impl<T: Iterator + Missing> HasMethod for T {
+    fn foo(self) {}
+}
+
+fn get_iter() -> impl Iterator {
+    core::iter::once(())
+}
+
+fn main() {
+    get_iter().foo();
+    //~^ ERROR the method `foo` exists for opaque type `impl Iterator`, but its trait bounds were not satisfied [E0599]
+}
diff --git a/tests/ui/iterators/iterator-does-not-need-into-iter.stderr b/tests/ui/iterators/iterator-does-not-need-into-iter.stderr
new file mode 100644
index 00000000000..3d3861e959f
--- /dev/null
+++ b/tests/ui/iterators/iterator-does-not-need-into-iter.stderr
@@ -0,0 +1,28 @@
+error[E0599]: the method `foo` exists for opaque type `impl Iterator`, but its trait bounds were not satisfied
+  --> $DIR/iterator-does-not-need-into-iter.rs:16:16
+   |
+LL |     get_iter().foo();
+   |                ^^^ method cannot be called on `impl Iterator` due to unsatisfied trait bounds
+   |
+note: the following trait bounds were not satisfied:
+      `&impl Iterator: Iterator`
+      `&impl Iterator: Missing`
+      `&mut impl Iterator: Missing`
+      `impl Iterator: Missing`
+  --> $DIR/iterator-does-not-need-into-iter.rs:7:9
+   |
+LL | impl<T: Iterator + Missing> HasMethod for T {
+   |         ^^^^^^^^   ^^^^^^^  ---------     -
+   |         |          |
+   |         |          unsatisfied trait bound introduced here
+   |         unsatisfied trait bound introduced here
+   = help: items from traits can only be used if the trait is implemented and in scope
+note: `HasMethod` defines an item `foo`, perhaps you need to implement it
+  --> $DIR/iterator-does-not-need-into-iter.rs:4:1
+   |
+LL | trait HasMethod {
+   | ^^^^^^^^^^^^^^^
+
+error: aborting due to 1 previous error
+
+For more information about this error, try `rustc --explain E0599`.