diff --git a/pytorch_lightning/loops/epoch/training_epoch_loop.py b/pytorch_lightning/loops/epoch/training_epoch_loop.py
index 97f80cc7e4c7e..fc5f8b9d11ece 100644
--- a/pytorch_lightning/loops/epoch/training_epoch_loop.py
+++ b/pytorch_lightning/loops/epoch/training_epoch_loop.py
@@ -11,6 +11,7 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
+import logging
 import math
 from collections import defaultdict
 from typing import Any, Dict, Generator, Iterator, List, Optional, overload, Tuple, Union
@@ -33,6 +34,8 @@
 from pytorch_lightning.utilities.signature_utils import is_param_in_hook_signature
 from pytorch_lightning.utilities.warnings import WarningCache
 
+log = logging.getLogger(__name__)
+
 _OUTPUTS_TYPE = List[_BATCH_OUTPUTS_TYPE]
 
 
@@ -100,6 +103,13 @@ def _is_validation_done(self) -> bool:
     @property
     def done(self) -> bool:
         """Evaluates when to leave the loop."""
+        if self.trainer.should_stop and self.min_steps:
+            self.trainer.should_stop = self.global_step >= self.min_steps
+            if not self.trainer.should_stop:
+                log.info(
+                    f"Trainer was signaled to stop but required minimum steps ({self.min_steps}) has not been met."
+                    " Training will continue..."
+                )
         return (self._is_training_done and self._is_validation_done) or self.trainer.should_stop
 
     def connect(  # type: ignore[override]
diff --git a/pytorch_lightning/loops/fit_loop.py b/pytorch_lightning/loops/fit_loop.py
index 8cbe4c167a29d..a369d863f33f2 100644
--- a/pytorch_lightning/loops/fit_loop.py
+++ b/pytorch_lightning/loops/fit_loop.py
@@ -167,28 +167,19 @@ def _results(self) -> _ResultCollection:
     @property
     def done(self) -> bool:
         """Evaluates when to leave the loop."""
-        # TODO(@awaelchli): Move track steps inside training loop and move part of these condition inside training loop
         stop_steps = _is_max_limit_reached(self.global_step, self.max_steps)
         # `processed` is increased before `on_train_epoch_end`, the hook where checkpoints are typically saved.
         # we use it here because the checkpoint data won't have `completed` increased yet
         stop_epochs = _is_max_limit_reached(self.epoch_progress.current.processed, self.max_epochs)
 
-        should_stop = False
-        if self.trainer.should_stop:
-            # early stopping
-            met_min_epochs = self.epoch_progress.current.processed >= self.min_epochs if self.min_epochs else True
-            met_min_steps = self.global_step >= self.min_steps if self.min_steps else True
-            if met_min_epochs and met_min_steps:
-                should_stop = True
-            else:
+        if self.trainer.should_stop and self.min_epochs:
+            self.trainer.should_stop = self.epoch_progress.current.processed >= self.min_epochs
+            if not self.trainer.should_stop:
                 log.info(
-                    "Trainer was signaled to stop but required minimum epochs"
-                    f" ({self.min_epochs}) or minimum steps ({self.min_steps}) has"
-                    " not been met. Training will continue..."
+                    f"Trainer was signaled to stop but required minimum epochs ({self.min_epochs}) has not been met."
+                    " Training will continue..."
                 )
-        self.trainer.should_stop = should_stop
-
-        return stop_steps or should_stop or stop_epochs or self.trainer.num_training_batches == 0
+        return stop_steps or self.trainer.should_stop or stop_epochs or self.trainer.num_training_batches == 0
 
     @property
     def skip(self) -> bool:
diff --git a/tests/trainer/test_trainer.py b/tests/trainer/test_trainer.py
index 587ff0b7b9f72..6fede8a612f21 100644
--- a/tests/trainer/test_trainer.py
+++ b/tests/trainer/test_trainer.py
@@ -610,7 +610,7 @@ def training_step(self, batch, batch_idx):
     with caplog.at_level(logging.INFO, logger="pytorch_lightning.trainer.trainer"):
         trainer.fit(model)
 
-    message = f"minimum epochs ({min_epochs}) or minimum steps (None) has not been met. Training will continue"
+    message = f"minimum epochs ({min_epochs}) has not been met. Training will continue"
     num_messages = sum(1 for record in caplog.records if message in record.message)
     assert num_messages == min_epochs - 2
     assert model.training_step_invoked == min_epochs * 2