The Japanese international signed a three-year deal with his present club in 2002, but has been persistently mentioned in the gossip columns with regards to a move away from Italy.
Atletico are long-term admirers of the 25-year-old's talents, and Nakamura admitted his attraction to the Spanish capital some time ago.
"It is an honour to know that a club like Atletico Madrid are interested in me," he said.
"The whole world respects that Spanish team and, if I were to choose a move there, it would be for sporting as well as financial reasons."
Reggina's supporters have been giving the midfielder a hard time recently, so a New Year move cannot be discounted, although Leeds would appear an extremely unlikely destination considering the economic climate at Elland Road, unless the Yorkshire club's board feel an Asian arrival would be smart business.
Leeds did reveal in the summer that they had investigated the possibility of raising their profile in the Far East with a high calibre capture from that part of the world.
"Finding and signing a quality player from the Far East this summer is definitely an ambition Peter Reid and I share," confirmed chairman Professor John McKenzie at the time.
Nakamura was left out of Reggina's side that faced Salernitana in midweek.
