Fellaini, a deadline day £27.5m signing from Everton, was United's only big-money purchase of the summer window.
But Berg, who played for United between 1997 and 2000, believes the Belgian international has the same kind of big-match pedigree as Old Trafford legend Cantona.
"He's not the kind of player to thread passes through but he has a sheer presence to hold the ball up, ability to win balls in the box and a match-winning mentality - he raises his game for the big matches," Berg was quoted as saying in the Daily Telegraph.
"Every game for United is a big one, so I think he will rise to that and enjoy it.
"When Cantona came, he had that mentality every game. I'm not saying he's going to be the same, but he can be."
The 25-year-old was not United's first choice target, after the club failed in bids for Ander Herrera and Cesc Fabregas.
He could make his United debut against Crystal Palace at Old Trafford on Saturday afternoon, with David Moyes hopeful he can upgrade a midfield that has come in for criticism early on this term.
Cantona, a cult figure at United after five hugely successful years, scored 64 league goals in 143 appearances under Sir Alex Ferguson.