Palace right-back Daniel Munoz had surgery on a similar injury in December and missed around six weeks.
The player is thought to be desperate to represent France at this summer’s World Cup and now faces a race against time to be passed fit.
And Glasner has now confirmed that they have decided against surgery for Mateta, though he will still miss about a month.
“Fortunately, he doesn’t need surgery,” Glasner revealed. “The injury is not as bad as feared, and so we think – and the opinion from several specialists and doctors – is that we can deal with the knee in a better way than with surgery.
“He will miss a certain time – I can’t say two weeks, three weeks or four weeks – but he doesn’t need surgery, that’s very positive, so hopefully he’s back soon.”
Sidelined: Jean-Philippe Mateta
Glasner continued, acknowledging that it would be a blow to lose Mateta for so long.
“Of course it’s a disappointment, but now he’s looking forward to the next months and it’s good for him that a final decision has been taken. Of course, in the end he took the final decision, with the recommendation of all the specialists and our medical department.
“He will have the next \[stage of\] rehab here at the training ground, and he wants to be back as soon as possible and contribute to achieve our goals. That’s his mindset, and I think that’s the best he can do.”
On Mateta’s failed move to Milan, Glasner added: "It was a disappointment but he is looking forward to the next months. It is good for him now that there is a final decision taken.
“Of course at the end he took the final decision with the recommendations with specialists and the medical departments, so they will do the rehab here at the training ground.
"He wants to be back as soon as possible and contribute to achieve our goals. That is his mindset and I think that is the best he can do."