The winger is said to have been in advanced talks with the Croatian side this winter and ready to move on loan to take the next step in his development.
However, Barcelona are eager for him to stay and have made that clear to Rodriguez, according to Mundo Deportivo.
The club are pushing for promotion this season and want Rodriguez to stay and help their bid, particularly as they are without several key players in attack due to injury.
Barca have also sent the same message to Guille Fernandez, who has also been linked with a winter exit due to a lack of game time.