The Red Devils boss is optimistic that the 34-year-old, whose current deal is set to expire in the summer, will commit to another season at Old Trafford just like Ryan Giggs
The former West Ham and Leeds United defender, 34, has long insisted that he wants to stay with the current Premier League leader.
When asked by reporters if Ferdinand will follow in the footsteps of veteran Ryan Giggs, who penned a one-year extension on Friday, Sir Alex responded: "That is a strong possibility.
"Rio has had a great season, he has managed himself the right way and we have contributed to that in the preparation we give him.
"He doesn’t play every game in the same way that Ryan doesn’t play every game. Two weeks ago, against Real Madrid, Rio was excellent. We need to get him ready for the big one on Tuesday."
United hosts Jose Mourinho's Spanish champions in the second leg of their Champions League round of 16 tie at Old Trafford on Tuesday, having earned a 1-1 draw at the Bernabeu in the first leg.
Before that, the Red Devils have the chance to extend their lead at the top of the Premier League table to 15 points over rivals Manchester City by defeating Norwich at home on Saturday.