diff --git a/doc/whatsnew/2/2.14/full.rst b/doc/whatsnew/2/2.14/full.rst
index 25864d655c..ec885c2299 100644
--- a/doc/whatsnew/2/2.14/full.rst
+++ b/doc/whatsnew/2/2.14/full.rst
@@ -5,6 +5,11 @@ What's New in Pylint 2.14.1?
 ----------------------------
 Release date: TBA
 
+* Avoid reporting ``unnecessary-dict-index-lookup`` or ``unnecessary-list-index-lookup``
+  when the index lookup is part of a destructuring assignment.
+
+  Closes #6788
+
 * Fixed parsing of unrelated options in ``tox.ini``.
 
   Closes #6800
diff --git a/pylint/checkers/refactoring/refactoring_checker.py b/pylint/checkers/refactoring/refactoring_checker.py
index 480078df8c..66773e2b38 100644
--- a/pylint/checkers/refactoring/refactoring_checker.py
+++ b/pylint/checkers/refactoring/refactoring_checker.py
@@ -160,6 +160,25 @@ def _will_be_released_automatically(node: nodes.Call) -> bool:
     return func.qname() in callables_taking_care_of_exit
 
 
+def _is_part_of_assignment_target(node: nodes.NodeNG) -> bool:
+    """Check whether use of a variable is happening as part of the left-hand
+    side of an assignment.
+
+    This requires recursive checking, because destructuring assignment can have
+    arbitrarily nested tuples and lists to unpack.
+    """
+    if isinstance(node.parent, nodes.Assign):
+        return node in node.parent.targets
+
+    if isinstance(node.parent, nodes.AugAssign):
+        return node == node.parent.target
+
+    if isinstance(node.parent, (nodes.Tuple, nodes.List)):
+        return _is_part_of_assignment_target(node.parent)
+
+    return False
+
+
 class ConsiderUsingWithStack(NamedTuple):
     """Stack for objects that may potentially trigger a R1732 message
     if they are not used in a ``with`` block later on.
@@ -1917,15 +1936,13 @@ def _check_unnecessary_dict_index_lookup(
 
                     value = subscript.slice
 
-                    if isinstance(node, nodes.For) and (
-                        isinstance(subscript.parent, nodes.Assign)
-                        and subscript in subscript.parent.targets
-                        or isinstance(subscript.parent, nodes.AugAssign)
-                        and subscript == subscript.parent.target
+                    if isinstance(node, nodes.For) and _is_part_of_assignment_target(
+                        subscript
                     ):
                         # Ignore this subscript if it is the target of an assignment
                         # Early termination; after reassignment dict index lookup will be necessary
                         return
+
                     if isinstance(subscript.parent, nodes.Delete):
                         # Ignore this subscript if it's used with the delete keyword
                         return
@@ -2017,11 +2034,8 @@ def _check_unnecessary_list_index_lookup(
         )
         for child in children:
             for subscript in child.nodes_of_class(nodes.Subscript):
-                if isinstance(node, nodes.For) and (
-                    isinstance(subscript.parent, nodes.Assign)
-                    and subscript in subscript.parent.targets
-                    or isinstance(subscript.parent, nodes.AugAssign)
-                    and subscript == subscript.parent.target
+                if isinstance(node, nodes.For) and _is_part_of_assignment_target(
+                    subscript
                 ):
                     # Ignore this subscript if it is the target of an assignment
                     # Early termination; after reassignment index lookup will be necessary
diff --git a/tests/functional/u/unnecessary/unnecessary_dict_index_lookup.py b/tests/functional/u/unnecessary/unnecessary_dict_index_lookup.py
index 7ae5488ce7..79f9f6a351 100644
--- a/tests/functional/u/unnecessary/unnecessary_dict_index_lookup.py
+++ b/tests/functional/u/unnecessary/unnecessary_dict_index_lookup.py
@@ -119,3 +119,8 @@ class Foo:
 for input_output in d.items():
     f.input_output = input_output  # pylint: disable=attribute-defined-outside-init
     print(d[f.input_output[0]])
+
+# Regression test for https://github.com/PyCQA/pylint/issues/6788
+d = {'a': 1, 'b': 2, 'c': 3}
+for key, val in d.items():
+    ([d[key], x], y) = ([1, 2], 3)
diff --git a/tests/functional/u/unnecessary/unnecessary_list_index_lookup.py b/tests/functional/u/unnecessary/unnecessary_list_index_lookup.py
index ba99d3b9ba..355d42a7f0 100644
--- a/tests/functional/u/unnecessary/unnecessary_list_index_lookup.py
+++ b/tests/functional/u/unnecessary/unnecessary_list_index_lookup.py
@@ -53,3 +53,12 @@ def process_list_again(data):
 # Regression test for https://github.com/PyCQA/pylint/issues/6603
 for i, num in enumerate():  # raises TypeError, but shouldn't crash pylint
     pass
+
+# Regression test for https://github.com/PyCQA/pylint/issues/6788
+num_list = [1, 2, 3]
+for a, b in enumerate(num_list):
+    num_list[a], _ = (2, 1)
+
+num_list = [1, 2, 3]
+for a, b in enumerate(num_list):
+    ([x, num_list[a]], _) = ([5, 6], 1)