The Palace No. 7 featured off the bench for the final quarter-of-an-hour of last weekend’s defeat to Manchester City at Selhurst Park, his first appearance since sustaining an injury in early February.
And Glasner confirmed that, ahead of this weekend’s trip to face Liverpool at Anfield, Olise’s recovery is progressing as hoped.
“He’s closer [to starting] than the week before,” the manager said at his pre-match press conference. “He had the whole week training with us.
“We’ve had a very good week in training, high quality and a lot of intensity, which is very important because Liverpool are maybe that team in the world that plays with the highest pressure – you never have time.
“It’s been a really good week and Michael was part of it, so he’s close to starting.
"I think Michael can't win the game alone, but he has a big role, and all the others have a big role. We'll need a great goalkeeper because Liverpool are a very attacking team, so everybody has a key role and we will show it again that we are competitive as a team.
"It's important to be it for 95-100 minutes, performing at our best level, but this week was really good."
The manager also confirmed that centre-back Marc Guéhi, injured in the same game as Olise, is expected to be available for selection in the closing weeks of the season.
Glasner said: “I can’t say when, but he’s working hard, we’re working hard, and of course we give our best. It’s a week where we have three games, so maybe it's the week after, but we hope, at latest, against Manchester United [on 6th May].”
Elsewhere, Glasner confirmed that Jaïro Riedewald – absent from matchday squads since mid-February – could make a return at Anfield.
He said: “We have no new injuries, but Jaïro is coming back. He trained the whole week with us and he could be in the squad on Sunday.
“You always have to be careful because if a player is out for five, six or seven weeks, and it's not like he can have one week's training and play 90 minutes. He will have to find his rhythm, like all the other injured players.
“It’s good that at the end of the season we're getting options back. We also hope that next week, or in the next two weeks, one, two, three players are coming back.”