With his deal due to expire in June, it has been suggested the Austrian has already decided to walk away at the end of the season.
However, while refusing to answer questions about the Manchester United job, Glasner has left the door open to extending his Palace deal.
Before facing Aston Villa on Wednesday night, the Eagles boss said: “I think in the next weeks, we will intensify the talks. With Macclesfield, Friday again, we go up north, and then everyone gets three days off after Macclesfield and then we have to target four regular weeks and in those weeks we will intensify the talks and I expect to find a final decision.
“There has been speculation since I arrived. So, believe me, I don't really care about it. I can sign today, or a player can sign a contract extension today and leave in summer. That's why for me, the length of a contract in these times doesn't say anything about your future.
“How long does Brennan's contract last? Four and a half years? So, if you sign a four-year contract, you can't honestly expect that you're always having the same manager, and I think that's why a player never signs just for a manager, he signs for a club, for the vision of a club. It’s not Oliver Glasner.
“Of course, you want to hear from the actual manager but that doesn't mean this lasts forever."