The Reds missed out on a record-extending 20th title last term by the narrowest of margins and Carrick says the Dutchman's arrival should ensure United don't end up disappointed again next May.
"He had a terrific season [with Arsenal] and he will further strengthen our squad," Carrick told reporters following England's 2-1 win against Italy on Wednesday night. "It's a great boost going into the new season.
"He's a world-class player and we've 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!"
It should be stressed that the deal to bring van Persie to Old Trafford hasn't quite been rubber-stamped just yet. The player still needs to agree personal terms and pass a medical.
But that hasn't stopped both players and fans from expressing their delight at what would be one of Manchester United's most sensational transfer coups.
"If it goes through, it will be brilliant," Carrick said. "But the club has always had strength in depth and it is about the squad and not the 11 on the pitch."