Both men are linked with moves to Old Trafford this summer with manager Jose Mourinho keen to revamp the squad ahead of a return to the Champions League.
French striker Griezmann has been speaking openly about his future this week and suggested the likelihood of him completing the move was “six out of 10′.
Real Madrid forward Rodriguez also has an uncertain future amid interest from United chiefs.
But former United defender Ferdinand believes that Griezmann would offer far more to United that Rodriguez at this moment.
“For what Manchester United need, I would go for Griezmann,” Ferdinand said on BT Sport.
“They’ve got [Henrikh] Mkhitaryan and [Juan] Mata – players who can play in that number 10 role, where Rodriguez likes to operate – so I would go for Griezmann.”
Griezmann admitted this week that it is the right time to leave Atleti after three seasons with the club.
However, Atletico president Enrique Cerezo does not believe that United will be prepared to pay the £85million release clause that they are requiring to let him leave.
“There has been no approach from Manchester United and nobody has offered to pay the clause and I don’t think anyone will,” he told Radio RMC.
“The situation is that Antoine Griezmann is an Atletico Madrid player and he has a contract until 2021.
“Never has he told me that he wants to leave.”