The Dutch goal machine is expected to finalise a deal with United within 24 hours subject to a medical and agreeing personal terms.
Carrick claimed that he heard the news of an offer being agreed for the player in the England dressing room ahead of the game with Italy on Wednesday night.
He told the Evening Standard: "Someone mentioned in the dressing room about Van Persie and if it goes through, it will be brilliant.
"He had a terrific season and he will further strengthen our squad. It is a great boost going into the new season.
"He is a world class player and we have always been about bringing in players of that ability.
"Can it make the difference between second and first? There wasn't much difference so hopefully we can go that step further!
"But the club has always had strength in depth and it is about the squad and not the 11 on the pitch."