The 21 year old centre back, who was the subject of intense transfer speculation last summer, only signed a new five-year deal back in August 2014.
But such has been Stones’ progression into a key component of Roberto Martinez‘s side, the Toffees are set to re-evaluate the terms of his current deal once the January transfer window closes.
Oviedo, whose contract runs out at the end of the current campaign, has endured another injury plagued season on Merseyside.
But the Club has the option to extend his deal by another 12 months, and the Echo claims that Everton’s backroom team will look to pursue this avenue.
And Besic – starter in Everton’s last three matches – is set to be handed an improved deal after impressing against Manchester City twice and Dagenham and Redbridge in the past ten days.