diff --git a/src/Psalm/Internal/Analyzer/Statements/Expression/CallAnalyzer.php b/src/Psalm/Internal/Analyzer/Statements/Expression/CallAnalyzer.php
index a39312d14..2d17a1faa 100644
--- a/src/Psalm/Internal/Analyzer/Statements/Expression/CallAnalyzer.php
+++ b/src/Psalm/Internal/Analyzer/Statements/Expression/CallAnalyzer.php
@@ -1386,8 +1386,8 @@ class CallAnalyzer
             $fleshed_out_type = ExpressionAnalyzer::fleshOutType(
                 $codebase,
                 $param_type,
-                $fq_class_name,
-                $fq_class_name
+                $fq_class_name ?: $context->self,
+                $fq_class_name ?: $context->self
             );
 
             if ($arg->unpack) {
diff --git a/src/Psalm/Internal/Analyzer/Statements/ExpressionAnalyzer.php b/src/Psalm/Internal/Analyzer/Statements/ExpressionAnalyzer.php
index 54729eeba..dd4d51ab6 100644
--- a/src/Psalm/Internal/Analyzer/Statements/ExpressionAnalyzer.php
+++ b/src/Psalm/Internal/Analyzer/Statements/ExpressionAnalyzer.php
@@ -976,6 +976,15 @@ class ExpressionAnalyzer
                         );
                     }
 
+                    $return_type->value = $self_class;
+                } elseif ($return_type_lc === 'parent') {
+                    if (!$self_class) {
+                        throw new \UnexpectedValueException(
+                            'Cannot handle ' . $return_type->value . ' when $self_class is empty'
+                        );
+                    }
+                    var_dump('here');
+
                     $return_type->value = $self_class;
                 } else {
                     $return_type->value = $codebase->classlikes->getUnAliasedName($return_type->value);
diff --git a/tests/CallableTest.php b/tests/CallableTest.php
index 2a25500cc..f0e066925 100644
--- a/tests/CallableTest.php
+++ b/tests/CallableTest.php
@@ -677,6 +677,31 @@ class CallableTest extends TestCase
                     /** @psalm-suppress UndefinedClass */
                     array_map(["two", "three"], ["one", "two"]);',
             ],
+            'callableSelfArg' => [
+                '<?php
+                    class Clazz {
+                        /**
+                         * @param callable(static) $f
+                         */
+                        function func1(callable $f): void {
+                            $f($this);
+                        }
+
+                        /**
+                         * @param callable(self) $f
+                         */
+                        function func2(callable $f): void {
+                            $f($this);
+                        }
+
+                        /**
+                         * @param callable(parent) $f
+                         */
+                        function func3(callable $f): void {
+                            $f($this);
+                        }
+                    }',
+            ],
         ];
     }