Reports from Japan have suggested that Yokohama Marinos, for whom Nakamura made his professional debut in 1997, are keen to bring the 30-year-old playmaker back in January ahead of the start of the 2009 J-League season.
But Strachan, speaking in the build-up to Celtic's Scottish League Cup quarter-final tie away to Kilmarnock on Wednesday, said: "It is the same statement as on Friday, the same position.
"Nobody has mentioned anything to me and unless anyone tells me anything different to my face then I will refer you to Friday's statement," he added. "I had a long conversation with Naka on Thursday and he never said a thing about that.
"I can only deal with reality; I will leave it up to the rest to deal with the nonsense that goes with it."
Nakamura's contract expires at the end of the current Scottish season and last week Strachan told Scotland's Daily Record newspaper: "Knowing Shunsuke, he would not upset anyone at this club one way or another.
"He wouldn't upset his team-mates, manager or coaches and I'd think he'd put the club before himself."
Andreas Hinkel, Celtic's Germany international defender, added Wednesday he hoped Nakamura would, at the very least, see out his contract.
"He would leave a big gap if he went but we hope that he stays. He is very good and technically one of the best, he is very confident with the ball and plays almost always the right pass.
"He has a lot of experience and is very important for us."