But the England striker is expected to be fit in time to face Klinsmann's former club Bayern Munich in the Champions League quarter-final first-leg at the Allianz Arena next Tuesday.
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And he believes that United forward is now a genuine contender to become the fourth Old Trafford star to be crowned European Footballer of the Year after Ronaldo, George Best, Bobby Charlton and Denis Law.
Klinsmann told Uefa.com: "So far, Wayne is playing a tremendous season. He's really hungry for goals, and he wants trophies now.
'He looks calm; he looks confident. So if he continues like that, he might get a shot at the European Player of the Year award.
"His instinct is just tremendous. He can smell the ball; he knows where it goes, and he's always available for the team.
'He works hard, he runs backwards and helps defensively. He lives in the moment, and that's the best thing you can do as a football player."
United are favourites to beat Bayern, but Klinsmann insists that the Champions League last eight is too close to call.
He said: 'Real Madrid are out, and now surprisingly Chelsea are out as well, but it still leaves some big clubs.
"Inter Milan; I think they look very strong, because they did really well in the game against Chelsea.
"And then you have Barcelona. It depends how hungry Barcelona are to follow up on the same great performance they did last season.
'United look really good, Arsenal look really good, Bayern Münich are through to the quarter-finals so you have teams that are all basically on the same level, and it will be decided on [who is] the hungriest."