McGowan has been linked with a move to China and will not play in the Clydesdale Bank Premier League match with Hibernian on Thursday, despite yet to agree to the switch.
McGlynn said: "The club have accepted a bid for Ryan so he won't play any part in the game tomorrow.
"He's not put pen to paper. It's disappointing to lose him but if good offers come in we need to accept them."
McGowan, a William Hill Scottish Cup winner in May, has been an ever-present at financial-troubled Hearts this season.
McGlynn was uncertain of the club involved, but believes they are Shanghai-based.
The offer for McGowan is understood to be worth in the region of £400,000 to Hearts, who are mired in financial difficulty.
The 23-year-old, who has been at Hearts since 2006, was seen at the club's west Edinburgh training base on Wednesday to say his goodbyes to his team-mates and support staff.
"Since I've been here he's played every single minute of every single game," said McGlynn, who was appointed boss last summer.
"He's been a massive influence both on and off the pitch. He's a really, really good character.
"He's a great lad, so he'll be a big miss."