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Former Brentford and Tottenham boss Thomas Frank is in advanced talks over taking over at Crystal Palace.
Sunday's 3-1 defeat by Liverpool was their fourth successive loss in the Premier League, with Pierre Sage's side having won just two of their 10 league matches this season.
Crystal Palace are without a win in the league since 11 October, with their losing run sparked by a 5-0 loss to fierce rivals Brighton. They also hold the worst defensive record in the league, having conceded 24 goals in 10 games.
The Eagles are also 21st in the Europa League table, with only one win from their four matches so far.
Sage was appointed on a three-year contract in June after Oliver Glasner departed at the end of last season.
The Frenchman had previously led Lens to a second-place finish in Ligue 1 and a first French Cup triumph in their 120-year history.
However, he has been unable to replicate Glasner's success at Selhurst Park. Glasner, who now manages Nottingham Forest, led the club to a first FA Cup title and a Conference League triumph.
After the Brighton defeat, Sage said that he felt "shame" from the result and admitted he did not know if he would be given the time to turn their fortunes around.
However, there was a degree of sympathy from some behind the scenes at Selhurst Park in the immediate aftermath.
Injuries were not kind to his plans, while the absence of Jean-Philippe Mateta and Ismaila Sarr - due to a mixture of fitness and personal issues related to both players' desire to leave the club - did not help the start of his reign.