He said: "I've watched United on television this season, and they've been doing very well," Kanchelskis said. "They lost at Bolton, and they've got a lot of injuries at the moment, but they've still got a good chance of winning the league.
"Of course, it will be difficult, because Arsenal are a very good team, with quality all the way through. But when United played at The Emirates earlier this month, they should have won the game.
"I think it will come down to a straight fight between United and Arsenal. And in that fight, I would say that United have a very good chance of winning.
"But I don't think Chelsea will be serious contenders this season. After losing Jose Mourinho and bringing in a new coach, they are going through a transitional stage. For me, they have left themselves with too much to do."
On comparisons with United winger Cristiano Ronaldo, Kanchelskis told the Manchester Evening News: "I'm just an ex-player, that's a question you would need to put to a coach. What I will say is that Cristiano Ronaldo is now a much, much better player than he was when he first arrived, because he has learned to play for the team.
"During his first season, he seemed to be playing for himself too much; there were too many tricks. Football is about 11 players, not one.
"But now he has developed as a player, and you can see the effect he has on the field for United."