diff --git a/pkg/objstore/cos/cos.go b/pkg/objstore/cos/cos.go
index 37bfef6b03..91529db2a5 100644
--- a/pkg/objstore/cos/cos.go
+++ b/pkg/objstore/cos/cos.go
@@ -333,8 +333,19 @@ func (b *Bucket) getRange(ctx context.Context, name string, off, length int64) (
 		runutil.ExhaustCloseWithLogOnErr(b.logger, resp.Body, "cos get range obj close")
 		return nil, err
 	}
+	// Add size info into reader to pass it to Upload function.
+	r := objectSizerReadCloser{ReadCloser: resp.Body, size: resp.ContentLength}
+	return r, nil
+}
+
+type objectSizerReadCloser struct {
+	io.ReadCloser
+	size int64
+}
 
-	return resp.Body, nil
+// ObjectSize implement objstore.ObjectSizer.
+func (o objectSizerReadCloser) ObjectSize() (int64, error) {
+	return o.size, nil
 }
 
 // Get returns a reader for the given object name.
diff --git a/pkg/objstore/objstore.go b/pkg/objstore/objstore.go
index 500b86a5ea..5089e492e0 100644
--- a/pkg/objstore/objstore.go
+++ b/pkg/objstore/objstore.go
@@ -492,6 +492,8 @@ func (b *metricBucket) Name() string {
 
 type timingReadCloser struct {
 	io.ReadCloser
+	objSize    int64
+	objSizeErr error
 
 	alreadyGotErr bool
 
@@ -506,8 +508,11 @@ func newTimingReadCloser(rc io.ReadCloser, op string, dur *prometheus.HistogramV
 	// Initialize the metrics with 0.
 	dur.WithLabelValues(op)
 	failed.WithLabelValues(op)
+	objSize, objSizeErr := TryToGetSize(rc)
 	return &timingReadCloser{
 		ReadCloser:        rc,
+		objSize:           objSize,
+		objSizeErr:        objSizeErr,
 		start:             time.Now(),
 		op:                op,
 		duration:          dur,
@@ -516,6 +521,10 @@ func newTimingReadCloser(rc io.ReadCloser, op string, dur *prometheus.HistogramV
 	}
 }
 
+func (t *timingReadCloser) ObjectSize() (int64, error) {
+	return t.objSize, t.objSizeErr
+}
+
 func (rc *timingReadCloser) Close() error {
 	err := rc.ReadCloser.Close()
 	if !rc.alreadyGotErr && err != nil {
diff --git a/pkg/objstore/objstore_test.go b/pkg/objstore/objstore_test.go
index acd46a93f5..e57e23324e 100644
--- a/pkg/objstore/objstore_test.go
+++ b/pkg/objstore/objstore_test.go
@@ -86,3 +86,30 @@ func TestTracingReader(t *testing.T) {
 	testutil.Ok(t, err)
 	testutil.Equals(t, int64(11), size)
 }
+
+func TestTimingTracingReader(t *testing.T) {
+	m := BucketWithMetrics("", NewInMemBucket(), nil)
+	r := bytes.NewReader([]byte("hello world"))
+
+	tr := NopCloserWithSize(r)
+	tr = newTimingReadCloser(tr, "", m.opsDuration, m.opsFailures, func(err error) bool {
+		return false
+	})
+	tr = newTracingReadCloser(tr, nil)
+
+	size, err := TryToGetSize(tr)
+
+	testutil.Ok(t, err)
+	testutil.Equals(t, int64(11), size)
+
+	smallBuf := make([]byte, 4)
+	n, err := io.ReadFull(tr, smallBuf)
+	testutil.Ok(t, err)
+	testutil.Equals(t, 4, n)
+
+	// Verify that size is still the same, after reading 4 bytes.
+	size, err = TryToGetSize(tr)
+
+	testutil.Ok(t, err)
+	testutil.Equals(t, int64(11), size)
+}