Van Persie is expected to make the switch from Arsenal to United in the next 24 hours after the two clubs agreed a fee for the 29-year-old.
Carrick heard the news after making his England comeback in the friendly international with Italy in Berne which Roy Hodgson's side won 2-1.
He said: "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."
Carrick, who replaced Frank Lampard as skipper for the last 20 minutes, also praised the performance of debutant Tom Cleverley alongside side in midfield.
He said: "He was fantastic and I had no doubts that he would have a good game.
"I have seen him every day in training at United and know how good he is and, with his personality, he is ideal for the big occasion.
"He has got a good grounding at United and had played in big games already before Wednesday's game."
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England came from behind to triumph thanks to goals from Phil Jagielka and Jermain Defoe.
Carrick said: "It was special for me to play after so long since I wore the jersey.
"To be captain for the first time in the final part of the game as well also made me feel proud."
Carrick's last appearance was in May 2010 against Mexico.