The midfielder is entering the final year of his current deal.
The Daly Echo says Corkâ€™s future appeared to be in some doubt early in the season, after he lost his place in the team to summer signing Victor Wanyama.
But, after the Â£12.5m man suffered an injury in December, Cork took his chance, re-establishing himself alongside Morgan Schneiderlin in the defensive midfield area.
The 24-year-oldâ€™s performances since his return have been so impressive that he was even name-checked by the England manager, Roy Hodgson, recently.
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