Fellaini has struggled with life in Manchester since arriving for more than £27million back in the summer on transfer deadline day.
The central midfield area was identified as a weakness by boss David Moyes when he took over at the club and nothing has changed with a quiet summer on the transfer front.
However Kompany belives that his compatriot Fellaini will impress United fans this season and he hopes that although he plays for a rival, his friend can get back to his best.
“People shouldn’t forget that it is Fellaini’s first season at Manchester United,” Kompany said.
“It’s a big move and he deserves some time – It will sound weird because he plays for the red half of the city but I want him to get back to his best.
“He’s an important player for Belgium. He’s one of those special players. You just feel he can have a big impact on the team. They will need him a lot.
“It’s just a matter of time really because he’s got the lot.”