Greening believes United are close to being a title challenger.
He told GrandNational: "If Paul Pogba stays, commits himself, he's happy and fit and wants to play there (at United) it will be immense for the team and a massive boost. Ole's said he only wants players who want to be at Manchester United.
"They definitely need another striker, maybe another centre half and then another player like a Jack Grealish or a James Madison who can play in wide areas as well as centrally. Then they've (United) have got a good chance of being title contenders again, without a shadow of a doubt."