Sunderland are keen to tie him down to a new deal, but it is understood that he has dismissed their latest offer.
It is thought that negotiations between the player and the club will continue, but that Colback will not decide his future until the summer.
This has alerted Everton, who are considering a move for the versatile ace if the situation deteriorates.
With Sunderland’s top flight status far from guaranteed, the Toffees are confident that staying in the top tier will be enough to tempt the one time England U-20 international to Merseyside.
The North East side are desperate to retain Colback, with the likes of Sebastian Larsson and Craig Gardner looking likely to leave.
The Swede is wanted by a host of top tier sides, while Leicester are tracking the ex-Birmingham man.