The 26-year-old has made 32 appearances across all competitions this season and has been among the standout performers for the overachieving side.
Standing at six-foot-three, Boyle is reportedly of interest to Wednesday’s League One rivals Portsmouth as well as Championship sides Preston North End and Huddersfield Town, where he served as an apprentice and made two senior appearances as a teenager.
A left-footed centre-half capable of playing out from the back, he would appear to fit Darren Moore’s preferred profile as the Owls look towards what looks likely to be a busy summer transfer window at S6.
As it stands, Dominic Iorfa is the only senior central defender contracted to the club looking ahead to next season. Bradford City captain Paudie O’Connor is among the other defenders under consideration by Wednesday.
Asked about Boyle’s situation, Cheltenham boss Michael Duff admitted Boyle had turned down a contract offer to stay at the Whaddon Road club and that he looked likely to leave when his current deal expires.
“He’s been great all season and if he goes, he deserves his move,” Duff said.
“I don’t think anyone can begrudge him his move for the service he’s given to the football club and the way he’s been around the place.
“I’ve not really had a conversation with him for a couple of months because he made it quite clear he didn’t want to sign it, no problem.”