diff --git a/haystack/core/errors.py b/haystack/core/errors.py
index d241b13084..b312f67230 100644
--- a/haystack/core/errors.py
+++ b/haystack/core/errors.py
@@ -31,7 +31,10 @@ class PipelineDrawingError(PipelineError):
 class PipelineMaxLoops(PipelineError):
     # NOTE: This is shown also when importing PipelineMaxComponentRuns, I can't find an easy
     # way to fix this, so I will ignore that case.
-    warnings.warn("PipelineMaxLoops is deprecated; use PipelineMaxComponentRuns instead.", DeprecationWarning)
+    warnings.warn(
+        "PipelineMaxLoops is deprecated and will be remove in version '2.7.0'; use PipelineMaxComponentRuns instead.",
+        DeprecationWarning,
+    )
 
 
 class PipelineMaxComponentRuns(PipelineMaxLoops):
diff --git a/haystack/core/pipeline/base.py b/haystack/core/pipeline/base.py
index af043928c1..727ebf58ff 100644
--- a/haystack/core/pipeline/base.py
+++ b/haystack/core/pipeline/base.py
@@ -42,6 +42,11 @@
 
 logger = logging.getLogger(__name__)
 
+_MAX_LOOPS_ALLOWED_DEPRECATION_MESSAGE = (
+    "'max_loops_allowed' argument is deprecated and will be removed in version '2.7.0'. "
+    "Use 'max_runs_per_component' instead."
+)
+
 
 class PipelineBase:
     """
@@ -65,7 +70,7 @@ def __init__(
             this dictionary can be serialized and deserialized if you wish to save this `Pipeline` to file.
         :param max_loops_allowed:
             How many times the `Pipeline` can run the same node before throwing an exception.
-            This is deprecated, use `max_runs_per_component` instead.
+            This is deprecated and will be removed in version 2.7.0, use `max_runs_per_component` instead.
         :param debug_path:
             When debug is enabled in `run()`, where to save the debug data.
         :param max_runs_per_component:
@@ -81,8 +86,7 @@ def __init__(
         self._debug_path = Path(debug_path)
 
         if max_loops_allowed is not None:
-            msg = "'max_loops_allowed' argument is deprecated. Use 'max_runs_per_component' instead."
-            warnings.warn(msg, DeprecationWarning)
+            warnings.warn(_MAX_LOOPS_ALLOWED_DEPRECATION_MESSAGE, DeprecationWarning)
             self._max_runs_per_component = max_loops_allowed
         else:
             self._max_runs_per_component = max_runs_per_component
@@ -96,8 +100,7 @@ def max_loops_allowed(self) -> int:
 
         :return: Maximum number of runs per Component
         """
-        msg = "'max_loops_allowed' argument is deprecated. Set 'max_runs_per_component' when initialising the Pipeline."
-        warnings.warn(msg, DeprecationWarning)
+        warnings.warn(_MAX_LOOPS_ALLOWED_DEPRECATION_MESSAGE, DeprecationWarning)
         return self._max_runs_per_component
 
     @max_loops_allowed.setter
@@ -109,8 +112,7 @@ def max_loops_allowed(self, value: int):
 
         :param value: Maximum number of runs per Component
         """
-        msg = "'max_loops_allowed' argument is deprecated. Set 'max_runs_per_component' when initialising the Pipeline."
-        warnings.warn(msg, DeprecationWarning)
+        warnings.warn(_MAX_LOOPS_ALLOWED_DEPRECATION_MESSAGE, DeprecationWarning)
         self._max_runs_per_component = value
 
     def __eq__(self, other) -> bool:
diff --git a/releasenotes/notes/deprecate_max_loops_allowed-2b17a9b442b68199.yaml b/releasenotes/notes/deprecate_max_loops_allowed-2b17a9b442b68199.yaml
index c140aca937..6cce5d8648 100644
--- a/releasenotes/notes/deprecate_max_loops_allowed-2b17a9b442b68199.yaml
+++ b/releasenotes/notes/deprecate_max_loops_allowed-2b17a9b442b68199.yaml
@@ -7,6 +7,6 @@ enhancements:
     Add new `PipelineMaxLoops` to reflect new `max_runs_per_component` init argument
 deprecations:
   - |
-    `Pipeline` init argument `max_loops_allowed` is deprecated in favor of `max_runs_per_component`.
+    `Pipeline` init argument `max_loops_allowed` is deprecated and will be remove in version `2.7.0`. Use `max_runs_per_component` instead.
   - |
-    `PipelineMaxLoops` exception is deprecated in favor of `PipelineMaxComponentRuns`.
+    `PipelineMaxLoops` exception is deprecated and will be remove in version `2.7.0`. Use `PipelineMaxComponentRuns` instead.