The Latics are 19th in the League One table and are currently a point above the relegation zone.
After an indifferent start to the season, Oldham lost just one in six during an impressive run, but recent home defeats to Tranmere and Bury have seen the club slide back down the division.
"There comes a point when you need to look closely at what's happening," Corney told the club's official website. "We are being dragged into a relegation battle. It is a concern to me and I don't want to get into a situation where it's too late.
"I still have faith in Paul, but we definitely have to sort some things out. I haven't fallen out with the manager. Paul and I have a very good relationship.
"It doesn't mean I have to agree with everything Paul does, and I can assure you that Paul doesn't agree with everything that I do."