The Yorkshire clubs have apparently been keeping tabs on the player.
It is now being reported that as well as the well-known interest from his first team Rangers there is interest from Yorkshire.
Championship sides Leeds United and Rotherham United are now being linked with a move for the player.
The BBC Scottish gossip column state the Express as reporting that Leeds and Rotherham are keen on the player.
Stewart has had an excellent two seasons with Dundee and this year has been nominated for the SPFA Players Player of the Year award.
Leeds did make a move for a top Scottish talent last summer, when Lee Erwin arrived from Motherwell.
Rotherham will be looking to improve their squad after a fantastic revival at the end of this season under Neil Warnock saw them miraculously fight off relegation from the Championship.
Leeds need another winger and a number ten, two positions that Stewart thrives in and he would potentially be a top arrival in the Championship.