Mateta saw a move to AC Milan fall through at the end of the transfer window because medical tests revealed a knee problem on deadline day.
However, following an examination on Monday, the striker will not go under the knife to address the issue as revealed by Glasner in his latest press conference.
"It's important for him now that it's clear he will be a Crystal Palace player, at least until the summer.
"Right now, he doesn't need surgery, so it is clear what we need to do in the next couple of weeks. Clarity is the most important thing.”
The France international is now joined by club-record signing Jorgen Strand Larsen who arrived from Wolves in the winter window.
Mateta is Palace’s joint top scorer alongside Ismaila Sarr with 10 goals in all competitions, and Glasner believes he is ready to give his all for the team when he returns.
"I am 100% convinced that JP will give us his best when he wears the Eagles shirt again.
"I think he deserves the best support, and I am pretty sure our fans will support him in the best way. They appreciate what he has done for Crystal Palace."
Reports suggest he could be available to return for Palace after March’s international break as he recovers from injury, meaning he may be back on the pitch for the clash against Leeds United.