HITC Sport reported the Owls' interest last month and Forest won't put up a fight, it seems.
The 30-year-old is currently in his second spell at the City Ground, having returned to the club with whom he'd spent four years previously from Celtic in 2013.
But the report claims that Wilson, who is one of the club's highest earners, won't be offered a new deal as part of a 'payroll blitz'.
Forest remain under a transfer embargo and also have midfielders Andy Reid and Robert Tesche out of contract this summer, with several loan deals due to expire.
HITC Sport reported last month that Wilson was a target for Forest's divisional rivals Sheffield Wednesday and a move to Hillsborough would see him reunite with former Parkhead teammates Glenn Loovens and Gary Hooper.
The Owls, who are looking good for a play-off place at present, may want to add to their defensive ranks with the futures of loan pair Michael Turner and Vincent Sasso uncertain.
Wilson is vastly experienced at Championship level, having racked up 152 appearances.