The defender was a key player for the Championship side last season.
The 25-year-old has been attracting interest from top flight newcomers Burnley, as well as from the Owls' Championship rivals Fulham and Derby County this summer, according to the Mail.
And perhaps fearing that an approach may be imminent - the Mail claims that the Clarets are ready to make a move if Michael Keane joins Leicester City - Wednesday have decided to offer the defender a bumper new contract.
Sheffield Wednesday manager Carlos Carvalhal
Keeping Lees at Hillsborough would undoubtedly be a big piece of business for Carlos Carvalhal this summer. The former Leeds United man has been a key player for the side over the last two seasons, helping them reach the play-off final during the last campaign.
And with the squad lacking depth in terms of central defensive options - utility man Sam Hutchinson has played there frequently during pre-season - it would be a major blow if Lees was to move on, especially as time is running out for a replacement to be found and the club's Championship campaign gets underway on Sunday.