Crystal Palace have been frustrated in attempts to persuade Kieran McKenna to replace Roy Hodgson but hope the Ipswich manager could take over at the end of the season. Hodgson remains under pressure after Monday’s late defeat by Chelsea left Palace five points clear of the relegation zone before their trip to 18th-placed Everton next Monday.

The Palace chairman, Steve Parish, is understood to have spoken to McKenna’s representatives but McKenna is believed to be unwilling to consider leaving while his side, in fourth place, are challenging for promotion in the Championship.

Related: ‘A bad period’: Crystal Palace can survive despite slump, insists Roy Hodgson

Parish is a long-term admirer of the 37-year-old former Manchester United assistant, who moved to Portman Road in December 2021 and signed a new four-year contract after leading Ipswich to promotion last season. Any move for McKenna, who is also thought to be a contender to take over at West Ham should they not renew David Moyes’s contract at the end of the season, would require a club to pay significant compensation.

Parish would prefer to wait until the summer before replacing Hodgson but has contemplated sacking the 76-year-old on more than one occasion during a run of four wins in the past 18 league matches that has dragged Palace into a relegation battle. He is understood to have sounded out several candidates in the past few weeks, including the former Nottingham Forest manager Steve Cooper and Julen Lopetegui, formerly of Wolves.

A series of banners at Selhurst Park criticising the ownership for “weak club culture and direction” were held up by a section of supporters during the televised game against Chelsea and are unlikely have gone down well in the boardroom after similar banners were displayed during the 4-1 defeat by Palace’s arch-rivals Brighton and a 5-0 thrashing at Arsenal.

Monday’s trip to Goodison Park – where Palace have not won since September 2014 – and the home game against Burnley could prove vital for Hodgson’s future given they are against sides in the bottom three.

Hodgson said after the Chelsea defeat: “I want to emphasise that there’s no complacency here … But if the question is: ‘Do I think that this group of players are good enough to get us out now?’ I do. I think they showed a lot [against Chelsea] which gives me even more faith and belief.”

McKenna said last week when asked about stories linking him to Palace: “My full focus and commitment is with Ipswich and the season that we’re having and the next game ahead.”