The former Manchester City man limped out of a friendly with Nottingham Forest earlier this month in his first public appearance for the club.
"Joleon Lescott is still not training. He is still suffering with a knee problem," he told reporters. "We don't think it is anything major but he has a bit of fluid on his knee.
"We are hopeful he will be back soon. He has done a bit more - but it is a tall order. It depends what happens over the next nine days but if you're asking me now whether [Lescott will] make it, it is 'probably not'."
Fellow new recruit Sebastien Pocognoli is expected to recover from multiple injuries to feature against Gus Poyet's side, although Gareth McAuley looks set to miss out with a calf problem.
"Sebastien has multiple injuries. He will be fine - there was no reason to risk him at Port Vale [on Tuesday] - and I suspect he will train and be available for Saturday," Irvine added.
"Gareth McAuley trained [on Wednesday] but it was asking far too much for him to be involved on Tuesday. Hopefully he will be training again [on Thursday].
"I think making the first game of the season is a big ask for Gareth to be perfectly honest."