That is the opinion of Sky Sports pundit Jamie Carragher, who adds that James Wilson is sure to get a taste of first-team action under Louis van Gaal next season.
Falcao linked up with the Red Devils last summer on a one-year loan deal with the view to a permanent stay.
However, reports claim that the Colombia international will head back to France, with the likes of Chelsea, Liverpool and Juventus all said to be interested.
Van Persie's Old Trafford future is also under the spotlight following the Dutchman's haul of 10 goals in 26 appearances.
But Carragher reckons that Van Persie will still have a role to play at United next season, adding that he would be surprised if Falcao was kept on.
He explained: "I don’t see Falcao there next season. With Van Persie, I think they’ll keep him. They’d find it difficult to move him on, although I don’t think they’d want to.
GETTY
Jamie Carragher reckons Radamel Falcao will leave Man Utd at the end of the season
I’d be very surprised if Falcao was still at Manchester United
Jamie Carragher
"With the system they’re playing at the moment Wayne Rooney’s the number one striker, but you’ve still got Van Persie to come in behind him, and that’s fantastic back-up.
"They can push each other, and at times I’m sure Rooney will play in midfield with Van Persie up front. They’ve still got young James Wilson as well.
"So I still see Van Persie there next season, because if they did move him on they’d still have to go and buy someone, but I’d be very surprised if Falcao was still at Manchester United."
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