The Eagles will be looking to reach the FA Cup semi-finals for the second time in four seasons when they travel to Craven Cottage.
They will be bolstered by the return of their top scorer, who was injured in the fifth-round win over Millwall at Selhurst Park earlier this month.
Glasner said of Mateta: “He trains now for two weeks with us, of course, always with his protection, and it’s also important for him to train a little bit.
“We had an internal game during the international break and he could play 60 minutes without any problems, so he’s ready.”
The Frenchman will be wearing protective headgear, the manager confirmed, joking: “I said it looks a little bit strange, but he says he feels comfortable, so let’s see! When he scores a header tomorrow it was the right mask, the right protection!”
On the squad’s wider fitness following the March international break – and ahead of Palace’s first competitive fixture in three weeks – Glasner explained: “The positive thing is all players are fit and available – just Will Hughes is questionable.
“He’s a bit sick, so let’s see how the afternoon and the night will be.
“But all others arrived back from the national teams in very good shape, and all the players who are here are fit.
“It’s just Chadi Riad and Cheick Doucouré who are out for the rest of the season. All others are ready.”