Van Persie joined United from Arsenal last summer, and is on track to be the Premier League's leading goalscorer once again.
Ibrahimovic, meanwhile, famously won eight titles in a row for five different clubs in three countries until 2011, and Jol believes Van Persie can have the same effect.
"Van Persie is the main man," Jol said. "He sets them up with little flicks and combination football and he also scores the most goals.
"He scores over 30 goals a season and will be top scorer again, as he was last year. He is like Zlatan. Wherever he goes, they will be champions. Van Persie has that quality."
Jol's side were beaten by United 1-0 on Saturday, with Wayne Rooney outshining Van Persie, netting the winner in the 79th minute with a delightful curling effort. Their performance left no doubt in Jol's mind as to who will take out this season's title.
"I think they will win it (the league title) this year because players like Rooney make the difference," Jol added.
"It is almost frightening the players they can bring on. This time it was Danny Welbeck, who is one of the quickest players in the Premier League. They bring him on just to hurt you.
"They not only have the best team, they have the best squad as well. But they are Manchester United, why shouldn't they have good players on the bench."
Information from the Press Association was used in this report.