Real Madrid remain interested in the Frenchman despite the closure of the English transfer window, ruling out the signing of a potential United replacement.
"I think he will stay, he would have gone by now. They would have replaced him and now they don't need to, that's the key thing," McClaren told Sky Sports News.
"You could see it on Sunday, Chelsea did really well against him in the first half, but once he got space in the second half, he can deliver the pass, score the goal. He can do things.
"When Ole first came in, he got the best out of Pogba for the first 15 games and the way he turned the game around against Manchester City, that's what he's capable of doing.
"Ole believes he can get the best out of him and especially with Maguire and the way they have started, Pogba might think 'yeah, I could be the king of this team'.
"These players want top players around them, to be challenging for the trophies. Manchester United demonstrated that with the summer signings [and] the first game.
"Pogba might be thinking 'they really want me and this is a good team, I could win things here'."