Miroslav Klose is frustrated by his lack of playing time at Lazio this season, but says he will not leave this winter.
Fernando Torres will join Milan permanently on January 5 ahead of his expected return to Atletico Madrid.
The 24-year-old midfielder plays for Jubilo Iwata in his homeland and Hoops boss Neil Lennon has previously spoken of his admiration for the player who has played twice for the Japanese national side this year.
The official Celtic website confirmed the player was training with the Scottish champions at Lennoxtown.
Lennon told the Daily Record earlier in the month: "We're looking to bring him over to take a look at him.
"John Park (head scout) has watched him a couple of times and we've seen some footage.
"However, it's always good to see him up against the rest of the players and how he copes with it.
"He can play left side or off the striker. He looks okay but we'll not have a real idea until we've seen him over here.
"I don't think there would be any money involved - he's a free."