The Austrian, having just led Palace to their FA Cup final triumph against Manchester City on Saturday, continues to be linked with RB Leipzig.
But Parish said: "Look, he will stay here for some period of time. He’ll be here next year and then we’ll take it from there.
"Of course I want him to stay longer but things happen in football and clubs evolve and move on.
"I’d love him to stay but the club’s got to develop behind him, and the club has to show the ambition in terms of what we want to do to move it forward, for people to feel part of something."
Contract talks underway
With a year to run on his deal, Parish was asked if Glasner would be offered new terms.
He responded: "We’ve been talking about it. For Oliver, it’s not about the things that maybe people think it’s about.
"Oliver wants to be part of something that’s going in a direction, same with all of us.
"I think that’s what we’ll talk about. I think obviously before finals it’s not a time for all of that. After finals is probably not a time for that.
"But somewhere down the track we’ll have a conversation and see what we all feel.
"Oliver will be here next year. Everybody knows length of his contract. Beyond that we’ll have to talk. It needs to be right for everybody."