Rashford, 28, has been away from his boyhood club for the past 18 months, first joining Aston Villa on loan and then Barcelona last summer.
Barcelona had a reported £26 million option to buy included in their loan deal, but decided against activating it, instead buying Anthony Gordon from Newcastle.
No other club has since come in for the England international, and it’s understood that Carrick is open to keeping him.
Rashford has since returned to Man United training following is participation in the 2026 World Cup.
Speaking after their friendly against Leeds United in Dublin on Wednesday (August 12), Carrick admitted that Rashford offers United “something a bit different.”
He said: "He's our player. He's come back great, like any other player. I've known him a long time, he gives us something a bit different.
"He's been in great spirits since he's been back, he's been back two or three days."