However, the Blues have no intention of selling the Scotland international and have firmly rebuffed both enquiries about their player.
It was thought that the player was keen on an exit from Goodison Park as he aims to be playing regular football ahead of the European Championships next summer, which Scotland have a strong chance of qualifying for.
His comments to the paper last month also suggested he could be considering a move as well, with him saying that he would have to "re-evaluate" if he wasn't playing that much.
However, that does not appear to be the case, with the Echo reporting that the 29-year-old remains happy at the club, and indeed, with life on Merseyside, despite having only featured from the bench in the Blues four games so far.
One big problem for Naismith at this moment in time is the so far impressive return of Arouna Kone. The Ivorian had looked surplus to requirements, but has since surged back and has been in fine form so far this season.
That sees Naismith fall further down the pecking order, and despite suggestions Everton aren't keen on a sale, he may fancy a move before tonight's deadline. That though, doesn't look likely at this moment in time.