Palace's next Premier League match is at Coventry on 21 November, after the international break.
The Eagles have won just two of their opening 10 games and hold the worst defensive record in the league, having conceded 24 goals.
Palace are winless in the league since 11 October. The losing run began with a 5-0 defeat by rivals Brighton.
Sunday's 3-1 defeat by Liverpool was Palace's fourth in succession in the Premier League.
Sage said afterwards that he felt"shame"from the defeat and admitted he did not know if he would be given time to turn Palace's fortunes around.
His failure to instil defensive robustness was a key factor in the sacking. He has been unable to replicate Glasner's success at the club.
Frank is viewed as the overwhelming favourite to replace Sage.
Frank was sacked by Tottenham in February after just under eight months in charge.
Palace believe Frank is the man to lead the club away from relegation trouble.
Fulham's results have picked up in recent weeks, and Palace have made their move.
Palace are also 21st in the 36-team Europa League table, with one win from their four matches.