diff --git a/qiskit/primitives/containers/data_bin.py b/qiskit/primitives/containers/data_bin.py
index 21252d2ef906..cb6efcc4f42c 100644
--- a/qiskit/primitives/containers/data_bin.py
+++ b/qiskit/primitives/containers/data_bin.py
@@ -103,9 +103,6 @@ def __init__(self, *, shape: ShapeInput = (), **data):
     def __len__(self):
         return len(self._data)
 
-    def __setattr__(self, *_):
-        raise NotImplementedError
-
     def __repr__(self):
         vals = [f"{name}={_value_repr(val)}" for name, val in self.items()]
         if self.ndim:
diff --git a/qiskit/primitives/primitive_job.py b/qiskit/primitives/primitive_job.py
index 64ab8d016095..580ab5930df5 100644
--- a/qiskit/primitives/primitive_job.py
+++ b/qiskit/primitives/primitive_job.py
@@ -35,6 +35,8 @@ def __init__(self, function, *args, **kwargs):
         super().__init__(str(uuid.uuid4()))
         self._future = None
         self._function = function
+        self._result = None
+        self._status = None
         self._args = args
         self._kwargs = kwargs
 
@@ -46,19 +48,31 @@ def _submit(self):
         self._future = executor.submit(self._function, *self._args, **self._kwargs)
         executor.shutdown(wait=False)
 
+    def _prepare_dump(self):
+        """This method allows PrimitiveJob to be serialized"""
+        _ = self.result()
+        _ = self.status()
+        self._future = None
+
     def result(self) -> ResultT:
-        self._check_submitted()
-        return self._future.result()
+        if self._result is None:
+            self._check_submitted()
+            self._result = self._future.result()
+        return self._result
 
     def status(self) -> JobStatus:
-        self._check_submitted()
-        if self._future.running():
-            return JobStatus.RUNNING
-        elif self._future.cancelled():
-            return JobStatus.CANCELLED
-        elif self._future.done() and self._future.exception() is None:
-            return JobStatus.DONE
-        return JobStatus.ERROR
+        if self._status is None:
+            self._check_submitted()
+            if self._future.running():
+                # we should not store status running because it is not completed
+                return JobStatus.RUNNING
+            elif self._future.cancelled():
+                self._status = JobStatus.CANCELLED
+            elif self._future.done() and self._future.exception() is None:
+                self._status = JobStatus.DONE
+            else:
+                self._status = JobStatus.ERROR
+        return self._status
 
     def _check_submitted(self):
         if self._future is None:
diff --git a/releasenotes/notes/serialize-primitive-job-aa97d0bf8221ea99.yaml b/releasenotes/notes/serialize-primitive-job-aa97d0bf8221ea99.yaml
new file mode 100644
index 000000000000..071de1e35a9d
--- /dev/null
+++ b/releasenotes/notes/serialize-primitive-job-aa97d0bf8221ea99.yaml
@@ -0,0 +1,5 @@
+---
+features_primitives:
+  - |
+    To make :class:`.PrimitiveJob` serializable, ``qiskit.primitives.containers.DataBin`` has been 
+    updated to be pickleable. As a result, :class:`.PrimitiveResult` is now also pickleable.