Van Persie and Carrick have been shortlisted for the main award, while Welbeck has been included in the Young Player category.
Sir Alex hopes at least one of his players will be celebrating when the winners are announced on Sunday 28 April.
"I'm delighted," the boss told MUTV. "They deserve to be nominated, there's no doubt about that. And I obviously hope one of them wins.
"Robin has had a fantastic season – his goals emphasise the impact he has made at our club. And I think this is Michael's best ever season at United. He's been absolutely magnificent. Both of them deserve to be there and I hope one of them wins it.
"It's amazing Michael has had to wait until he's 31 to get nominated for anything!" joked the boss. "He really deserves it.
"Danny has also shown some great performances this season for us and his country, and I'm delighted for him too."