The 21-year-old forward, who moved to the League One club in September 2012, is under contract at Boundary Park until 2015.
Johnson has confirmed that there has been interest shown in the former Everton player.
"We have had an approach and some interest in Jose and we have to decide whether or not it is right for the club," Johnson told Oldham's official website.
"It may not happen and I would say it is very much 50-50 at the moment. We have to decide whether it is right for all parties, whether we can replace him, and does he want to go or stay?
"Jose is a great player and we don't want to lose him. I am sure whether it is here or elsewhere, he will go on and do well in football because he is a good lad."
Baxter has scored 17 goals in 50 appearances for the Latics.