The Dutchman was stretchered off during the final moments of Wednesday's victory over Olympiakos but his compatriot has played down the gravity of the knock
Van Persie was stretchered off in the closing stages of Wednesday's win over Olympiakos, after the 30-year-old had scored a superb hat-trick to send his side through to the quarter-finals of the Champions League.
Speaking immediately after the game, David Moyes confirmed the striker had taken a knock on the knee, but Kluivert is confident that it is not serious.
He told Algemeen Dagblad: "Robin went right to the hospital on Thursday morning. His upper leg was quite stiff.
"We have to wait for the results, but we have high hopes that it's not a heavy injury. Maybe he can play against Manchester City next week."
Moyes's side produced a remarkable comeback to recover from a two-goal first-leg deficit and triumph 3-0 at Old Trafford to take their place in the last eight of the Champions League and Kluivert hailed United's attacking intent.
He added: "It was a wonderful match against Olympiakos. United really had to win to save their season.
"If you see them start like that, with a lot of pressure going forward, it's really impressive. Really nice to see as well.
"I have a lot of contact with Robin and I like watching him play. He deserved this. He was really keen on a good match on Wednesday.
"A few days earlier they got trashed by Liverpool, so they needed to answer, and that's just what United did, with Van Persie starring."