diff --git a/CHANGELOG.md b/CHANGELOG.md
index 5232cc793163f..92d9e899fa0df 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -147,7 +147,10 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 - Deprecated `DataModule` properties: `train_transforms`, `val_transforms`, `test_transforms`, `size`, `dims` ([#8851](https://github.com/PyTorchLightning/pytorch-lightning/pull/8851))
 
 
-- Deprecated `prepare_data_per_node` flag on Trainer and set it as a property of `DataHooks`, accessible in the `LightningModule` and `LightningDataModule` [#8958](https://github.com/PyTorchLightning/pytorch-lightning/pull/8958)
+- Deprecated `prepare_data_per_node` flag on Trainer and set it as a property of `DataHooks`, accessible in the `LightningModule` and `LightningDataModule` ([#8958](https://github.com/PyTorchLightning/pytorch-lightning/pull/8958))
+
+
+- Deprecated `log_gpu_memory` flag on the Trainer in favor of passing the `GPUStatsMonitor` callback to the Trainer ([#9124](https://github.com/PyTorchLightning/pytorch-lightning/pull/9124/))
 
 
 ### Removed
diff --git a/pytorch_lightning/trainer/connectors/logger_connector/logger_connector.py b/pytorch_lightning/trainer/connectors/logger_connector/logger_connector.py
index a965699510689..1392c07282942 100644
--- a/pytorch_lightning/trainer/connectors/logger_connector/logger_connector.py
+++ b/pytorch_lightning/trainer/connectors/logger_connector/logger_connector.py
@@ -24,11 +24,17 @@
 from pytorch_lightning.utilities.apply_func import apply_to_collection, move_data_to_device
 from pytorch_lightning.utilities.metrics import metrics_to_scalars
 from pytorch_lightning.utilities.types import _EVALUATE_OUTPUT
+from pytorch_lightning.utilities.warnings import rank_zero_deprecation
 
 
 class LoggerConnector:
     def __init__(self, trainer: "pl.Trainer", log_gpu_memory: Optional[str] = None) -> None:
         self.trainer = trainer
+        if log_gpu_memory is not None:
+            rank_zero_deprecation(
+                "Setting `log_gpu_memory` with the trainer flag is deprecated and will be removed in v1.7.0! "
+                "Please monitor GPU stats with the `GPUStatsMonitor` callback directly instead."
+            )
         self.log_gpu_memory = log_gpu_memory
         self.eval_loop_results = []
         self._val_log_step: int = 0
diff --git a/pytorch_lightning/trainer/trainer.py b/pytorch_lightning/trainer/trainer.py
index 7ebbc55ae7ac9..c1a3f0bcd0a32 100644
--- a/pytorch_lightning/trainer/trainer.py
+++ b/pytorch_lightning/trainer/trainer.py
@@ -236,6 +236,10 @@ def __init__(
 
             log_gpu_memory: None, 'min_max', 'all'. Might slow performance
 
+                .. deprecated:: v1.5
+                    Deprecated in v1.5.0 and will be removed in v1.7.0
+                    Please use the ``GPUStatsMonitor`` callback directly instead.
+
             log_every_n_steps: How often to log within steps (defaults to every 50 steps).
 
             prepare_data_per_node: If True, each LOCAL_RANK=0 will call prepare data.
diff --git a/tests/deprecated_api/test_remove_1-7.py b/tests/deprecated_api/test_remove_1-7.py
index 7581bf2b0c142..5fd26602f4b25 100644
--- a/tests/deprecated_api/test_remove_1-7.py
+++ b/tests/deprecated_api/test_remove_1-7.py
@@ -87,3 +87,10 @@ def test_v1_7_0_trainer_prepare_data_per_node(tmpdir):
         match="Setting `prepare_data_per_node` with the trainer flag is deprecated and will be removed in v1.7.0!"
     ):
         _ = Trainer(prepare_data_per_node=False)
+
+
+def test_v1_7_0_trainer_log_gpu_memory(tmpdir):
+    with pytest.deprecated_call(
+        match="Setting `log_gpu_memory` with the trainer flag is deprecated and will be removed in v1.7.0!"
+    ):
+        _ = Trainer(log_gpu_memory="min_max")