The Aussie shot-stopper is out of contract at the end of this Premier League season and there is continued speculation whether he will stay at Boro or move to another club, possibly elsewhere in Europe.
Speaking on the club's official website, Pears said, "We're not sure what Mark's future is here at the moment and that won't be decided until after the last game of the season.
"Our Premier League status is not secure yet and that is our main focus. The players are hurting, the fans are hurting and we need to put it right on Saturday.
"We won't know anything about Mark until after the Manchester City game and we will assess the situation when that happens."
Fellow Aussie keeper Brad Jones stepped up to the first team last week due to Schwarzer being out of the side for the last two games and second-string keeper Ross Turnbull injuring himself at training. Pears believes that if Schwarzer does happen to exit, then Jones is more than ready to fulfil his role.
"Brad has made two starts, all at the beginning of the season, and with the injuries he's had to his thigh and his finger it was a big ask to throw him straight in there.
"It's a huge pressure as a goalkeeper to play in the Premier League but Brad is no young lad anymore, he's 26, although he hasn't had that much experience, maybe only 30 games."