The want-away Arsenal captain has been heavily linked with a move to the Etihad Stadium after revealing he would not extend his contract and then refusing to take part in the Gunners' pre-season tour of Asia.
And the 26-year-old praised Van Persie's improvement in recent seasons, including a stunning campaign last term which saw him top the Premier League scoring charts.
"He’s a player who has improved so much," Kompany told reporters. "I started playing against him five or six years ago, but his performances last season were unbelievable.
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"He has led by example at Arsenal so, yes, he is a great player."
Van Persie has several other interested parties, including Manchester United and Juventus, making his signing with the champions far from a formality.
But, even if the Dutchman is not secured by Roberto Mancini, Kompany insists that City will still develop into an even better side.
"I think we will improve anyway," added the Belgian. "Whether we need new players is up to the manager.
"I only know that, even if we don’t, we will improve naturally anyway."