diff --git a/pytorch_lightning/trainer/distrib_parts.py b/pytorch_lightning/trainer/distrib_parts.py
index 7d5a00523ef9e..2d5b7f25c01f7 100644
--- a/pytorch_lightning/trainer/distrib_parts.py
+++ b/pytorch_lightning/trainer/distrib_parts.py
@@ -37,6 +37,7 @@
 from pytorch_lightning.utilities.exceptions import MisconfigurationException
 from pytorch_lightning.utilities.distributed import rank_zero_only
 from pytorch_lightning.utilities import rank_zero_warn
+from pytorch_lightning.utilities.memory import is_oom_error, garbage_collection_cuda
 
 try:
     from apex import amp
@@ -471,9 +472,46 @@ def pick_single_gpu(exclude_gpus: list):
     raise RuntimeError("No GPUs available.")
 
 
-def pick_multiple_gpus(nb):
+def pick_single_gpu_realist_workload(exclude_gpus: list, model: LightningModule) -> int:
+    batch = next(iter(model.train_dataloader()))
+    for i in range(torch.cuda.device_count()):
+        if i in exclude_gpus:
+            continue
+        # Try to allocate on device:
+        device = torch.device(f"cuda:{i}")
+        try:
+            with torch.set_grad_enabled(True):
+                model_device = model.to(device)
+                batch_device = tuple(itup.to(device) for itup in batch)
+                model_device.train()  # record grads
+                model_device.training_step(batch_device, 0)
+        except RuntimeError as exception:
+            if is_oom_error(exception):  # clean after the failed attempt
+                garbage_collection_cuda()
+            else:
+                raise
+            continue
+        return i
+    raise RuntimeError("None of the GPUs could accept the given workload.")
+
+
+def pick_multiple_gpus(nb: int, model: Optional[LightningModule] = None) -> list:
+    r""" Pick available GPUs
+
+    Args:
+        nb: the max number of GPU to pick
+        model: (optional) a LightningModule with model and train_loader attached
+
+    Return:
+        a list of GPU index availables
+
+    Note: if model is not None, a GPU is considered available if it is able to run in `train` mode a batch
+    """
     picked = []
     for _ in range(nb):
-        picked.append(pick_single_gpu(exclude_gpus=picked))
-
+        if not model:
+            picked.append(pick_single_gpu(exclude_gpus=picked))
+        else:
+            assert hasattr(model, 'train_dataloader')
+            picked.append(pick_single_gpu_realist_workload(exclude_gpus=picked, model=model))
     return picked
diff --git a/pytorch_lightning/trainer/trainer.py b/pytorch_lightning/trainer/trainer.py
index 4b342328df297..ba58cee894c67 100644
--- a/pytorch_lightning/trainer/trainer.py
+++ b/pytorch_lightning/trainer/trainer.py
@@ -493,6 +493,7 @@ def __init__(
         self.accumulate_grad_batches = accumulate_grad_batches
         self.configure_accumulated_gradients(accumulate_grad_batches)
 
+        self.auto_select_gpus = auto_select_gpus
         # for gpus allow int, string and gpu list
         if auto_select_gpus and isinstance(gpus, int):
             self.gpus = pick_multiple_gpus(gpus)
@@ -970,6 +971,10 @@ def fit(
             model.prepare_data()
             self._is_data_prepared = True
 
+        # Run updated auto GPU selection with the actual model/input data
+        if self.auto_select_gpus:
+            self.update_auto_selected_gpus(model)
+
         # Run auto batch size scaling
         if self.auto_scale_batch_size:
             if isinstance(self.auto_scale_batch_size, bool):
@@ -1407,6 +1412,15 @@ def call_setup_hook(self, model):
         self.setup(stage_name)
         model.setup(stage_name)
 
+    def update_auto_selected_gpus(self, model):
+        # Called when model/data is known. Ensure the GPU used have enough VRAM.
+        self.gpus = pick_multiple_gpus(len(self.gpus), model)  # At most the current number of GPUs
+
+        self.data_parallel_device_ids = _parse_gpu_ids(self.gpus)
+        self.root_gpu = determine_root_gpu_device(self.data_parallel_device_ids)
+        self.on_gpu = True if (self.data_parallel_device_ids and torch.cuda.is_available()) else False
+        self.set_nvidia_flags(self.is_slurm_managing_tasks, self.data_parallel_device_ids)
+
 
 class _PatchDataLoader(object):
     r"""
diff --git a/tests/trainer/test_trainer.py b/tests/trainer/test_trainer.py
index d6641c2f7ab24..2f9d3239fac48 100644
--- a/tests/trainer/test_trainer.py
+++ b/tests/trainer/test_trainer.py
@@ -748,13 +748,11 @@ def _optimizer_step(*args, **kwargs):
     trainer.fit(model)
 
 
+@pytest.mark.skipif(not torch.cuda.is_available(), reason="test requires GPU machine")
 def test_gpu_choice(tmpdir):
     trainer_options = dict(
         default_root_dir=tmpdir,
     )
-    # Only run if CUDA is available
-    if not torch.cuda.is_available():
-        return
 
     num_gpus = torch.cuda.device_count()
     Trainer(**trainer_options, gpus=num_gpus, auto_select_gpus=True)
@@ -763,6 +761,29 @@ def test_gpu_choice(tmpdir):
         Trainer(**trainer_options, gpus=num_gpus + 1, auto_select_gpus=True)
 
 
+@pytest.mark.skipif(not torch.cuda.is_available(), reason="test requires GPU machine")
+def test_gpu_choice_workload(tmpdir):
+    """ Test if the training is not allowed by `pick_single_gpu_realist_workload` by using an overly large batch-size
+    TODO: not adapted for new gen GPUs with very large VRAM
+    """
+    class CurrentModel(EvalModelTemplate):
+        def train_dataloader(self):
+            # Aim to overload the VRAM with the whole MNIST
+            from tests.base.datasets import MNIST
+            return torch.utils.data.DataLoader(MNIST(root=self.data_root, train=True, download=True), batch_size=60000)
+
+    model = CurrentModel()
+    trainer = Trainer(
+        max_steps=1,
+        max_epochs=1,
+        default_root_dir=tmpdir,
+        gpus=1,
+        auto_select_gpus=True,
+    )
+    with pytest.raises(RuntimeError, match=r'.*None of the GPUs could accept the given workload.*'):
+        trainer.fit(model)
+
+
 @pytest.mark.parametrize(['tpu_cores', 'expected_tpu_id', 'error_expected'], [
     pytest.param(1, None, False),
     pytest.param(8, None, False),