The Spain international has had a frustrating season because of ankle and knee problems, and Laudrup revealed the player will require surgery.
"He will need an operation at some stage," said Laudrup. "In the best case, it could be when he finishes his career. It could be at the end of the season, but it could be now.
"He has been struggling with his ankle as well as his knee. The professional he is, he wanted to play but in a lot of games he could not give 100 per cent.
"I said to him not to worry and just carry on but he wants to score goals and help the team. In the league he has not had the physical presence to do that and he has been worried about that.
"He is a very important player for us but if you are playing at 80 per cent then it is very frustrating and the performance is not what you wanted. It's been very frustrating for him.
"We have to be certain of what he needs to do and when, as the player always has the last word. If the player feels he is not even 90 per cent the final word will be his."
Laudrup is expecting a tough match with Everton, and he admits he has been hugely impressed with Roberto Martinez, who replaced David Moyes in the Goodison Park hotseat in the summer.
"He has done a great job. It is difficult to come into a club who have had the same manager for 11 years," Laudrup said.
"In the last ten years they are also around the top half of the league, and that was with a smaller budget that a lot of teams. So to come in and want to change the way of playing is even more difficult.
"I have watched their last four or five games and they were outstanding against Arsenal at the Emirates. They have kept a lot of their best players and made a huge signing in (Romelu) Lukaku on the final day of the transfer window."
Meanwhile, Laudrup insists he has no intention of quitting Swansea after his name was linked with the vacant post at Tottenham.
The Dane admits he is flattered to be included in the list of possible candidates to replace Andre Villas-Boas, who was sacked on Monday, but insists his he will stay at the Liberty Stadium.
Laudrup said: "You can always look at things from different perspectives. The positive one is when your name is linked as someone thinks you are doing well.
"It is always positive and flattering when others are talking about you and your name is linked with other clubs and Tottenham is a big club.
"But I would never leave a club, not Swansea or anyone, in the middle of a season. I have never done that as a player or as a manager and I will not do it in the future."
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