diff --git a/docs/rules/expect-expect.md b/docs/rules/expect-expect.md
index 6ba708903..b6ea9c1e6 100644
--- a/docs/rules/expect-expect.md
+++ b/docs/rules/expect-expect.md
@@ -75,3 +75,23 @@ test('returns sum', () =>
     .run();
 );
 ```
+
+Examples of **correct** code for deep assertion functions with the
+`{ "assertFunctionNames": ["expect", "tester.foo.expect"] }` option:
+
+```js
+/* eslint jest/expect-expect: ["error", { "assertFunctionNames": ["expect", "tester.foo.expect"] }] */
+test('nested expect method call', () => {
+  class Foo {
+    expect(k) {
+      return k;
+    }
+  }
+  let tester = {
+    foo: function() {
+      return new Foo();
+    },
+  };
+  tester.foo().expect(123);
+});
+```
diff --git a/src/rules/__tests__/expect-expect.test.ts b/src/rules/__tests__/expect-expect.test.ts
index 3ef7ed9a8..5513329ac 100644
--- a/src/rules/__tests__/expect-expect.test.ts
+++ b/src/rules/__tests__/expect-expect.test.ts
@@ -26,6 +26,33 @@ ruleTester.run('expect-expect', rule, {
       code: 'it("should return undefined",() => expectSaga(mySaga).returns());',
       options: [{ assertFunctionNames: ['expectSaga'] }],
     },
+    {
+      code: `test('verifies expect method call', () => {
+        class Foo {
+          expect(k) {
+            return k;
+          }
+        }
+        new Foo().expect(123);
+      });`,
+      options: [{ assertFunctionNames: ['Foo.expect'] }],
+    },
+    {
+      code: `test('verifies deep expect method call', () => {
+              class Foo {
+                expect(k) {
+                  return k;
+                }
+              }
+              let tester = {
+                  foo: function() {
+                      return new Foo()
+                  }
+              }
+              tester.foo().expect(123);
+            });`,
+      options: [{ assertFunctionNames: ['tester.foo.expect'] }],
+    },
     {
       code: [
         'test("verifies the function call", () => {',
diff --git a/src/rules/utils.ts b/src/rules/utils.ts
index 9cc2e7a03..c5b0a6eee 100644
--- a/src/rules/utils.ts
+++ b/src/rules/utils.ts
@@ -614,6 +614,10 @@ export function getNodeName(node: TSESTree.Node): string | null {
       break;
     case AST_NODE_TYPES.MemberExpression:
       return joinNames(getNodeName(node.object), getNodeName(node.property));
+    case AST_NODE_TYPES.NewExpression:
+      return getNodeName(node.callee);
+    case AST_NODE_TYPES.CallExpression:
+      return getNodeName(node.callee);
   }
 
   return null;