diff --git a/haystack/preview/document_stores/mixins.py b/haystack/preview/document_stores/mixins.py
index 7a17026104..e6a642479d 100644
--- a/haystack/preview/document_stores/mixins.py
+++ b/haystack/preview/document_stores/mixins.py
@@ -1,4 +1,4 @@
-from typing import List, Optional, Type
+from typing import List, Type
 
 
 from haystack.preview.document_stores.protocols import Store
@@ -6,28 +6,9 @@
 
 class StoreAwareMixin:
     """
-    Adds the capability of a component to use a single document store from the `self.store` property.
-
+    Signals to the pipeline that this component will need a store added to their input data.
     To use this mixin you must specify which document stores to support by setting a value to `supported_stores`.
     To support any document store, set it to `[Store]`.
     """
 
-    _store: Optional[Store] = None
     supported_stores: List[Type[Store]]  # type: ignore # (see https://github.com/python/mypy/issues/4717)
-
-    @property
-    def store(self) -> Optional[Store]:
-        return self._store
-
-    @store.setter
-    def store(self, store: Store):
-        if not store:
-            raise ValueError("Can't set the value of the store to None.")
-        if not isinstance(store, Store):
-            raise ValueError("'store' does not respect the Store Protocol.")
-        if not any(isinstance(store, type_) for type_ in type(self).supported_stores):
-            raise ValueError(
-                f"Store type '{type(store).__name__}' is not compatible with this component. "
-                f"Compatible store types: {[type_.__name__ for type_ in type(self).supported_stores]}"
-            )
-        self._store = store
diff --git a/haystack/preview/pipeline.py b/haystack/preview/pipeline.py
index 41dc0b5779..4e1f540241 100644
--- a/haystack/preview/pipeline.py
+++ b/haystack/preview/pipeline.py
@@ -2,6 +2,7 @@
 
 from pathlib import Path
 
+from canals.component import ComponentInput
 from canals.pipeline import (
     Pipeline as CanalsPipeline,
     PipelineError,
@@ -29,6 +30,7 @@ class Pipeline(CanalsPipeline):
     def __init__(self):
         super().__init__()
         self._stores: Dict[str, Store] = {}
+        self._store_connections: Dict[str, str] = {}
 
     def add_store(self, name: str, store: Store) -> None:
         """
@@ -94,13 +96,42 @@ def add_component(self, name: str, instance: Any, store: Optional[str] = None) -
                     f"Store named '{store}' not found. "
                     f"Add it with 'pipeline.add_store('{store}', <the docstore instance>)'."
                 )
-            instance.store = self._stores[store]
+
+            if not any(isinstance(self._stores[store], type_) for type_ in type(instance).supported_stores):
+                raise ValueError(
+                    f"Store type '{type(self._stores[store]).__name__}' is not compatible with this component. "
+                    f"Compatible store types: {[type_.__name__ for type_ in type(instance).supported_stores]}"
+                )
+
+            self._store_connections[name] = store
 
         elif store:
             raise ValueError(f"Component '{name}' doesn't support stores.")
 
         super().add_component(name, instance)
 
+    def run(self, data: Dict[str, Any], debug: bool = False) -> Dict[str, Any]:
+        """
+        Runs the pipeline.
+
+        Args:
+            data: the inputs to give to the input components of the Pipeline.
+            debug: whether to collect and return debug information.
+
+        Returns:
+            A dictionary with the outputs of the Pipeline.
+
+        Raises:
+            PipelineRuntimeError: if the any of the components fail or return unexpected output.
+        """
+        # Assigns the docstore to the input dataclasses of each component that requested it
+        for component_name, store_name in self._store_connections:
+            if not component_name in data:
+                data[component_name] = self.get_component(component_name).input()
+            data[component_name].store = self._stores[store_name]
+
+        super().run(data=data, debug=debug)
+
 
 def load_pipelines(path: Path, _reader: Optional[Callable[..., Any]] = None):
     return load_canals_pipelines(path=path, _reader=_reader)