The Dutchman, who has only one year left of his current deal at the Emirates Stadium, has said that he will not sign a new contract with the Gunners, which has sparked a race for his signature among Europe's elite.
While Manchester United appear to be the favourites to land the Gunners skipper, Kompany has admitted that the 29-year-old would be a good fit at the Premier League champions.
"He is a player who has improved so much. I started playing against him five or six years ago, but his performances last season were unbelievable," said Kompany.
"A player like this would be an incredible addition to any team that he joined. His movement is near perfection and the stats show his finishing. He has led by example at Arsenal, so yes, he is a great player.
"I think we will improve anyway, whether we need new players is up to the manager. I only know that, even if we don't, we will improve naturally anyway."
City begin their Premier League title defence at home to Southampton on Sunday.