diff --git a/CHANGELOG.md b/CHANGELOG.md
index 8d979b41893f5..6790579f4d0bc 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -26,6 +26,8 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 
 - Deprecated `filepath` in `ModelCheckpoint` ([#4213](https://github.com/PyTorchLightning/pytorch-lightning/pull/4213))
 
+- Deprecated `reorder` parameter of the `auc` metric ([#4237](https://github.com/PyTorchLightning/pytorch-lightning/pull/4237))
+
 ### Removed
 
 
diff --git a/pytorch_lightning/metrics/functional/classification.py b/pytorch_lightning/metrics/functional/classification.py
index abf661e46fb1b..a831611fb9593 100644
--- a/pytorch_lightning/metrics/functional/classification.py
+++ b/pytorch_lightning/metrics/functional/classification.py
@@ -806,7 +806,9 @@ def auc(
     Args:
         x: x-coordinates
         y: y-coordinates
-        reorder: reorder coordinates, so they are increasing
+        reorder: reorder coordinates, so they are increasing. The unstable algorithm of torch.argsort is
+            used internally to sort `x` which may in some cases cause inaccuracies in the result.
+            WARNING: Deprecated and will be removed in v1.1.
 
     Return:
         Tensor containing AUC score (float)
@@ -821,6 +823,11 @@ def auc(
     direction = 1.
 
     if reorder:
+        rank_zero_warn("The `reorder` parameter to `auc` has been deprecated and will be removed in v1.1"
+                       " Note that when `reorder` is True, the unstable algorithm of torch.argsort is"
+                       " used internally to sort 'x' which may in some cases cause inaccuracies"
+                       " in the result.",
+                       DeprecationWarning)
         # can't use lexsort here since it is not implemented for torch
         order = torch.argsort(x)
         x, y = x[order], y[order]
@@ -830,8 +837,9 @@ def auc(
             if (dx, 0).all():
                 direction = -1.
             else:
-                raise ValueError("Reordering is not turned on, and "
-                                 "the x array is not increasing: %s" % x)
+                # TODO: Update message on removing reorder
+                raise ValueError("Reorder is not turned on, and the 'x' array is"
+                                 f" neither increasing or decreasing: {x}")
 
     return direction * torch.trapz(y, x)
 
diff --git a/tests/test_deprecated.py b/tests/test_deprecated.py
index 70eb2a709b195..c8a7b1d270e35 100644
--- a/tests/test_deprecated.py
+++ b/tests/test_deprecated.py
@@ -5,6 +5,7 @@
 import torch
 
 from tests.base import EvalModelTemplate
+from pytorch_lightning.metrics.functional.classification import auc
 
 from pytorch_lightning.callbacks import ModelCheckpoint
 from pytorch_lightning.utilities.exceptions import MisconfigurationException
@@ -63,3 +64,8 @@ def test_dataloader(self):
 
     def test_end(self, outputs):
         return {'test_loss': torch.tensor(0.7)}
+
+
+def test_auc_reorder_remove_in_v1_1_0():
+    with pytest.deprecated_call(match='The `reorder` parameter to `auc` has been deprecated'):
+        _ = auc(torch.tensor([0, 1, 2, 3]), torch.tensor([0, 1, 2, 2]), reorder=True)