The 31-year-old, who can operate as an attacking midfielder or as a forward, was on the books of Rangers from 2007 and 2012 and was very successful during his spell at Ibrox.
The Scotland international is struggling for playing time at Norwich in the Championship in England at the moment, and the former Everton man admitted to The Daily Mail that returning to Rangers would appeal to him (click here to read more).
Rangers, though, have not made an approach for Naismith, according to The Scottish Sun.
It has been reported that the Gers have not made an enquiry for the Scotland international attacker - perhaps a sign that the Glasgow giants are not interested in him.
“The 31-year-old does have other options south of the border while several Premiership sides — though not Rangers — have also made enquiries,” adds the report in The Scottish Sun.