Croft joined the Latics last summer on a season-long loan from Derby but the move became a permanent transfer in January when his deal with the Rams was terminated.
The 27-year-old winger was offered fresh terms at Boundary Park but Oldham boss Lee Johnson told the club's official website: "I gave him a deadline which has now passed.
"As he has not replied, I expect him to sign for someone else and wish him all the best.
"I am hopeful of bringing in somebody of the same quality or even better."
Croft featured in 53 of Oldham's 54 matches this season, more than any other Latics player.