The Premier League champions have been heavily linked with a move for the 29-year-old Holland international but face stiff competition from rivals Manchester United.
Van Persie scored 30 league goals last season and Kompany acknowledges that, wherever the player ends up, he would be a welcome addition to the team.
"It's very easy to say you want to play next to Robin van Persie," Kompany told Sky Sports News as he prepares to face the Dutchman in an international friendly for Belgium on Wednesday evening.
"He's a great player. He's proved it so many times last season and any team he would play for he'd make it stronger."
The City skipper will line-up alongside one of Van Persie's Arsenal team-mates on Wednesday in Thomas Vermaelen.
Vermaelen does not feel Van Persie has been affected by the speculation and remains hopeful that his club captain will stay at the Emirates Stadium.
"To me he looks fit and sharp in training," said Vermaelen.
"He's working hard. He's working on his fitness. I don't see anything (different) and I hope he stays the next four years as well.
Asked if he thinks that will happen, the 26-year-old added: "I've no idea. I hope so. I don't know what happens behind the scenes but at the moment I can only say he's a player for Arsenal.
"I feel really positive for the new season. If we all stay fit, the squad is strong enough to compete for the title."