Vidic is the current skipper at Old Trafford but will be moving on at the end of the season and David Moyes will have to choose someone new to wear the armband.
Rooney is a leading candidate after this week putting pen to paper on a long-term contract extension to commit his future to United until 2019.
Vidic believes it was vital for the club to secure the striker's services and has given his support to the England international.
"Wayne is a big player and it is important for him to stay," Vidic told Sky Sports News after Rooney celebrated his new deal with a goal in Saturday's 2-0 victory at Crystal Palace.
"Wayne has signed a long-term contract and he will be one of the most important players in the next few years."
Questioned on the possibility of Rooney replacing him as captain, Vidic added: "Obviously it is the manager's decision and he has to choose his captain.
"Wayne is one of the leaders in the team and I will not be surprised if he becomes captain."