diff --git a/src/transformers/utils/quantization_config.py b/src/transformers/utils/quantization_config.py
index 9f0d55ff1a24..4a526ee6f717 100755
--- a/src/transformers/utils/quantization_config.py
+++ b/src/transformers/utils/quantization_config.py
@@ -25,7 +25,7 @@
 
 from packaging import version
 
-from ..utils import is_auto_awq_available, is_hqq_available, is_torch_available, is_torchao_available, logging
+from ..utils import is_auto_awq_available, is_hqq_available, is_torch_available, is_torchao_available, is_gptqmodel_available, logging
 
 
 if is_torch_available():
@@ -618,6 +618,7 @@ def __init__(
         desc_act: bool = False,
         sym: bool = True,
         true_sequential: bool = True,
+        backend: Optional[str] = None,
         checkpoint_format: Optional[str] = "gptq",
         use_cuda_fp16: bool = False,
         model_seqlen: Optional[int] = None,
@@ -641,6 +642,8 @@ def __init__(
         self.desc_act = desc_act
         self.sym = sym
         self.true_sequential = true_sequential
+        self.backend = backend
+        self.checkpoint_format = checkpoint_format
         self.use_cuda_fp16 = use_cuda_fp16
         self.model_seqlen = model_seqlen
         self.block_name_to_quantize = block_name_to_quantize
@@ -653,7 +656,6 @@ def __init__(
         self.disable_exllama = kwargs.pop("disable_exllama", None)
         self.cache_block_outputs = cache_block_outputs
         self.modules_in_block_to_quantize = modules_in_block_to_quantize
-        self.checkpoint_format = checkpoint_format
         self.post_init()
 
     def get_loading_attributes(self):
@@ -690,6 +692,10 @@ def post_init(self):
                     ['wikitext2','c4','c4-new'], but we found {self.dataset}"""
                 )
 
+        if self.backend is not None and not is_gptqmodel_available():
+            if self.backend == "auto_trainable":
+                self.use_exllama = False
+
         if self.disable_exllama is None and self.use_exllama is None:
             # New default behaviour
             self.use_exllama = True
@@ -736,6 +742,12 @@ def post_init(self):
                     "You current version of `optimum` does not support `modules_in_block_to_quantize` quantization argument, please upgrade `optimum` package to a version superior than 1.15.0 ."
                 )
 
+        if is_gptqmodel_available() and self.backend is None:
+            if self.exllama_config["version"] == ExllamaVersion.ONE and not self.use_exllama:
+                self.backend = "auto_trainable"
+            else:
+                self.backend = "auto"
+
     def to_dict(self):
         config_dict = super().to_dict()
         config_dict.pop("disable_exllama", None)