The Scottish Sun reported this week that Osman is a top target for Rangers boss Mark Warburton, who is desperate to replace the injured Niko Kranjcar - not to mention the departed Joey Barton - at Ibrox next month.
Rangers' Niko Kranjcar in action
Diego Fabbrini, Sergi Canos and Jota are among the many candidates mentioned so far, however, having been without a club since leaving Goodison Park in the summer, Osman would be a favourable option from a financial point of view.
That said, it does not appear as though the 35-year-old is planning an immediate return to the game, based on the following response.
"Have I?" asked Osman, when informed he had been linked with a move to Rangers.
The midfielder, who has been coaching Everton's youngsters, said of his physical condition: "Up until about a month ago I was in good nick and then Christmas started getting closer and closer - I’ve got to be honest, I’ve enjoyed that thoroughly so far.
Leon Osman in action for Everton
"I’m finding it [not playing] okay to be honest. I think I thought I’d have a meltdown once I had no football and I didn’t know what was happening, but I’ve actually enjoyed it. I’ve not missed it as much.
"Obviously, Saturday afternoons come and the three o’clock games are going on and you find you’re not there, but all in all I’m not doing too bad."
Rangers have found form of late, climbing to second in the Scottish Premiership.
However, Mark Warburton's side are already 16 points behind bitter rivals Celtic, who travel to Ibrox on Saturday afternoon.
Would Osman be a good signing for Glasgow Rangers?