The Japan international has hinted he may want to return to his homeland, and J.League club Yokohama Marinos, for whom Nakamura made his professional debut in 1997, will attempt to sign the 30-year-old midfielder in January ahead of their 2009 season.

In a tetchy game in Ayrshire, Nakamura suffered some heavy tackles by the Killie players after Scott McDonald headed Celtic into a 15th-minute lead.

He was booked by referee Craig Thomson for complaining about the treatment he was receiving before curling a free-kick past Alan Combe in the dying seconds of the first half.

Nakamura failed to appear for the second half after picking up an injury just above the knee and is fighting to be fit for the Clydesdale Bank Premier League match against Hearts at Tynecastle on Sunday.

Danny Invincibile pulled a goal back for Killie in the 67th minute but Aiden McGeady quickly restored Celtic's two-goal lead to take them into the last four alongside Rangers, Falkirk and Dundee United.

Afterwards Strachan praised the durability of Nakamura, saying: "No, I don't think things like that will make Naka want to go back.

"He is bigger and stronger than anything that anybody can chuck at him, that's for sure. He stiffened up and did well to last to half-time.

"He was very brave and it's crazy in this day and age that Naka is the one that gets booked.

"He reacted by saying he got tackled and he pointed four times. The referee obviously booked him because it was only three.

"If he is going to complain about tackles then he has to get it right!

"What Naka did was put the ball down and put it in the back of the net.

"That's the best way of answering anybody who wants to take you out of the game."

Kilmarnock manager Jim Jefferies admits he would be glad to see the back of Nakamura who, not for the first time, punished the Ayrshire side for conceding a free-kick within shooting distance.

He said: "I will drive him to the airport!

"Nakamura has fantastic technique and that's why we told the players not to give away free-kicks, although I didn't think it was a free-kick.

"But the referee gave it and you know it's always a possibility that he will score.

"If we had started the game the way we finished the first half it might have been different.

"But we gifted them a goal and that was disappointing.

"When we got it back to 2-1 we didn't do what we should have done, got the ball into the box and put them under pressure, and by not doing that, they broke away and showed a bit of quality to make it 3-1.

"That was the killer for us and we need to learn lessons."