Roy Hodgson is to remain in charge of Crystal Palace for now after holding talks with the chairman, Steve Parish, in the aftermath of their 5-0 thrashing against Arsenal, but he has been warned he could be sacked if results do not improve. It is understood Parish seriously considered parting company with the 76-year-old after seeing his side slump to the embarrassing defeat at the Emirates Stadium, with other board members believed to have been strongly in favour of Hodgson’s departure after one win in the past 12 matches. However, Parish decided after talks with Hodgson, in which he is understood to have offered “constructive criticism” to the former England manager about turning the club’s season around, that no change will be made before their next game, at home against Sheffield United next Tuesday. Hodgson is believed to have been made fully aware that failure to spark a revival against the Premier League’s bottom side could end in being shown the door. Palace have slipped to 15th place – only five points clear of Luton, who are in the relegation zone with a game in hand – and their following two games are away at their arch‑rivals Brighton and at home against Chelsea. If Hodgson survives the Sheffield United match, it is understood those games could determine whether he remains until the end of the season, when the contract he signed last summer expires. Julen Lopetegui and Steve Cooper are the favourites to replace Hodgson if he is sacked. Graham Potter – who was spotted at the Arsenal game – was sounded out with Cooper for the post in the summer. Palace are reported to have held talks with the football club sale specialists Raine in an effort to raise funds to help with the redevelopment of Selhurst Park, where planning permission has been granted for the £150m main stand. Building work is due to start this year but spiralling costs mean about £45m in extra funding is required. Palace have had a bid for the Colombia right-back Daniel Muñoz rejected by the Belgian club Genk but are expected to return with a new offer. The 27-year-old defender is valued at €10m (£8.6m).