diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index 193356a46a6ea..9e48e8bb35838 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -190,6 +190,7 @@ representation of :class:`DataFrame` objects (:issue:`4889`).
 
 Other enhancements
 ^^^^^^^^^^^^^^^^^^
+- :meth:`concat` will preserve the ``attrs`` when it is the same for all objects and discard the ``attrs`` when they are different. (:issue:`41828`)
 - :class:`DataFrameGroupBy` operations with ``as_index=False`` now correctly retain ``ExtensionDtype`` dtypes for columns being grouped on (:issue:`41373`)
 - Add support for assigning values to ``by`` argument in :meth:`DataFrame.plot.hist` and :meth:`DataFrame.plot.box` (:issue:`15079`)
 - :meth:`Series.sample`, :meth:`DataFrame.sample`, and :meth:`.GroupBy.sample` now accept a ``np.random.Generator`` as input to ``random_state``. A generator will be more performant, especially with ``replace=False`` (:issue:`38100`)
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 4aff7acc4c6fb..7f18399160cad 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -5522,6 +5522,12 @@ def __finalize__(
                 object.__setattr__(self, name, getattr(other, name, None))
 
         if method == "concat":
+            attrs = other.objs[0].attrs
+            check_attrs = all(objs.attrs == attrs for objs in other.objs[1:])
+            if check_attrs:
+                for name in attrs:
+                    self.attrs[name] = attrs[name]
+
             allows_duplicate_labels = all(
                 x.flags.allows_duplicate_labels for x in other.objs
             )
diff --git a/pandas/tests/generic/test_finalize.py b/pandas/tests/generic/test_finalize.py
index 135e8cc7b7aba..f27e92a55268f 100644
--- a/pandas/tests/generic/test_finalize.py
+++ b/pandas/tests/generic/test_finalize.py
@@ -758,7 +758,6 @@ def test_groupby_finalize(obj, method):
     "method",
     [
         lambda x: x.agg(["sum", "count"]),
-        lambda x: x.transform(lambda y: y),
         lambda x: x.apply(lambda y: y),
         lambda x: x.agg("std"),
         lambda x: x.agg("var"),
diff --git a/pandas/tests/reshape/concat/test_concat.py b/pandas/tests/reshape/concat/test_concat.py
index 676571e419a1a..c4b32371042b3 100644
--- a/pandas/tests/reshape/concat/test_concat.py
+++ b/pandas/tests/reshape/concat/test_concat.py
@@ -698,3 +698,49 @@ def test_concat_posargs_deprecation():
         result = concat([df, df2], 0)
     expected = DataFrame([[1, 2, 3], [4, 5, 6]], index=["a", "b"])
     tm.assert_frame_equal(result, expected)
+
+
+@pytest.mark.parametrize(
+    "data",
+    [
+        Series(data=[1, 2]),
+        DataFrame(
+            data={
+                "col1": [1, 2],
+            }
+        ),
+        DataFrame(dtype=float),
+        Series(dtype=float),
+    ],
+)
+def test_concat_drop_attrs(data):
+    # GH#41828
+    df1 = data.copy()
+    df1.attrs = {1: 1}
+    df2 = data.copy()
+    df2.attrs = {1: 2}
+    df = concat([df1, df2])
+    assert len(df.attrs) == 0
+
+
+@pytest.mark.parametrize(
+    "data",
+    [
+        Series(data=[1, 2]),
+        DataFrame(
+            data={
+                "col1": [1, 2],
+            }
+        ),
+        DataFrame(dtype=float),
+        Series(dtype=float),
+    ],
+)
+def test_concat_retain_attrs(data):
+    # GH#41828
+    df1 = data.copy()
+    df1.attrs = {1: 1}
+    df2 = data.copy()
+    df2.attrs = {1: 1}
+    df = concat([df1, df2])
+    assert df.attrs[1] == 1