The 28-year-old striker, who has just a year remaining on his current contract, is refusing to sign a new deal at Arsenal this summer, prompting interest from City, Manchester United and Juventus.
Kompany has been impressed by Van Persie’s development since the Belgian defender moved to the Premier League, with the Netherlands striker scoring 37 goals last season.
“He’s 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.”
Kompany captained the Eastlands outfit to their first Premier League title in May, ending the club’s 44-year wait for the top-flight crown.
The City skipper, who made 31 league appearances last season, was rewarded for his contribution to the club’s successful campaign with a new six-year deal at The Etihad in July.
“I have signed a six-year deal, so there are six titles possible within those years, so you know what? I want to get them all,” he added.
“It probably won’t happen, but we will see in six years’ time. I will try everything for that.”
Kompany has scored six times in 160 appearances for City after former manager Mark Hughes signed the centre-half from Hamburg in a £6.5m deal in August 2008.
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