The 31-year-old, who can operate as an attacking midfielder or as a forward, has been linked with a return to Rangers in the January transfer window.
According to Sky Sports, Rangers are considering making a move for the Scotland international attacker.
It has also been reported that the Gers’ Scottish Premiership rivals Heart of Midlothian, have made contact with Norwich in the Championship in England over the availability of the former Kilmarnock star.
Naismith has said that there has been no contact with Rangers, but the Scotsman has suggested that he is open to joining Graeme Murty’s side in the January transfer window.
Naismith wrote on BBC Sport: “There have been a lot of stories linking me with two of my old clubs, Kilmarnock and Rangers. I have not spoken to either of them, but I am not ruling out any clubs at this stage.
“I have not hidden the fact that I am definitely going back to play in Scotland one day. Whether that is sooner or later, we will wait and see.
“But it is something I really want to do. I want to go back when I have something to give and feel I can contribute and be a big success.”
Rangers are third in the Scottish Premiership table at the moment with 40 points from 22 matches.
Graeme Murty’s side are 11 points behind leaders and Old Firm rivals Celtic and three points behind second-placed Aberdeen.