Glasner revealed that the game would come too soon for injured trio Adam Wharton, Ismaïla Sarr and Eddie Nketiah, who will miss out.
However, there was better news in regards a potential Selhurst Park bow for new signing Yeremy Pino, who made his debut off the bench in the win over Aston Villa.
In addition, new arrivals Christantus Uche and Jaydee Canvot also have a chance of being involved against Sunderland.
The manager told his pre-match press conference: "Fortunately, all the international players came back healthy and fit so that everybody of them is available. The injured players are progressing very well.
"At the moment it looks like Adam Wharton, Ismaïla Sarr and Eddie Nketiah are available at least against Liverpool, so in two weeks. That's a great job from our medical department.
"Tomorrow none of them are available. Millwall, none of them is available, maybe Adam and Eddie have a chance for West Ham.
“We have 18 fit on-field players – and all the new signings will be in the squad tomorrow. There is a good chance that Yeremy [Pino] makes his starting debut for Crystal Palace tomorrow.
"He just needed to rest during the international break. The first week of the international break he didn't train. He had a small injury from his last game at Villarreal. But then he started preparing on Monday."
Longer-term absentees Chadi Riad and Cheick Doucouré also remain unavailable.
Match Details
Crystal Palace v Sunderland
- Saturday, 13th September
- 15:00 BST
- Premier League
- Selhurst Park
- Live audio commentary on Palace TV+.