Everton's hierarchy do not believe sacking Frank Lampard will improve their prospects of staying in the Premier League at this stage, despite the increasing threat of the club's first relegation from the top flight in 71 years.
That is not to say Everton have decided to stick with Lampard until the end of the season, irrespective of results.
There is real concern about Everton's predicament at board level, Sky Sports News has been told, with the club having lost six of their last seven Premier League games.
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Rumours about a possible return for Sam Allardyce are wide of the mark, Sky Sports News has been told.
Nevertheless, it is thought that independent intermediaries outside of the club have been sounding out other managerial options, should the Everton board decide to make a change.
Asked about his future in his press conference on Friday, Lampard said: "I know the rules, I have no problem with that. In my relatively short management career I spent 18 months at Chelsea where I was always probably two games from the sack.
"I'm proud to be manager here and keep the history of this club going in a positive way.
"The fans live and breathe this club. I've only been here five minutes but I do too."
Were Everton to be relegated, they would find themselves in significant financial difficulty, with very few members of the first-team squad on contracts that automatically reduce if the club finds itself in the Championship, Sky Sports News understands.
That would likely mean a complete overhaul of the squad would be inevitable.
Last month Everton revealed a £121m loss for the period to June 2021 - the third successive year of deficits in excess of £100m.
Their accounts took another big hit when the EU and UK sanctioned one of the club's key sponsors, Alisher Usmanov, leading to Everton suspending sponsorship deals with Russian companies USM, Megafon and Yota.
That shows how much the club relies on the cash injected by owner Farhad Moshiri, whose patience will be severely tested if Everton drop out of the top division for the first time since 1951.
'Perilously close to the doomsday scenario'
Former Everton defender Alan Stubbs told Sky Sports after the Burnley defeat:
"In terms of giving the players a boost and some breathing space, it was a huge game. How damaging it proves, only time will tell. I said prior to the match that it was a game Everton couldn't afford to lose.
"After getting themselves in a really good position, unfortunately like many other games this season they've found a way to lose the game.
"Getting on a run of losing is the same as when you're winning. You don't think about it but psychologically when you're losing, with each game that goes by you start to doubt yourself more and make the wrong decisions.
"That's what Everton have found themselves in now. For an opposition manager to say at half-time that this team doesn't know how to win a game of football away from home, that tells you everything you need to know about the state Everton are in.
"They had chances to win and realistically should've won the game, but they've done this on numerous occasions this season where they've not been able to see out games and their defending has been of a really poor standard that has let the opposition back into games.
"It's quite depressing as an Everton fan when you look at the fixtures - it's difficult to say where the points are going to come from. Everton have got a result out of nowhere in the past and so it wouldn't surprise me if on Saturday at home [to Manchester United] they were to get a result.
"But I'm not very hopeful. Brentford at home and Watford away is not going to be easy so you start scratching your head. For Everton to be in this position at this stage of the season is incredible to digest.
"There's a few fans saying Frank Lampard has got a few decisions wrong, but at the end of the day, these are the same players who have been with the managers before him. It's not about getting rid of Frank Lampard now.
"It's about the players trying to do whatever is necessary to get a result and get Everton out of the mess they're in. Too much blame has been placed on managers but there is so much wrong at Everton right now - from boardroom level right the way through to the pitch.
"The players have got to somehow find enough desire and spirit to get Everton through this season and keep them in the league. It is perilously close to the doomsday scenario. This is the most fearful I've ever been as an Everton fan."
Southall: Everton players are too nice
Former Everton goalkeeper Neville Southall:
"Everton are making silly mistakes that are costing them. If you score two goals away from home, you expect to win the game. When you're in a relegation battle, you either expect your goalkeeper to be rubbish, which he's not or for him to be man of the match every week - which he hasn't been - so there must be positives.
"In the media, there's been a lot of focus on the negatives but we've got 27 points to play for and we've got Manchester United on Saturday. As a kid growing up, that's who you want to play against to show what good a player you are.
"There's no point looking backwards. My heart is telling me they will stay up while my head is saying they will struggle. Dominic Calvert-Lewin is bound to score eventually and it's about taking the pressure off the players now during the week in training.
"The players need to remember that at the end of the season they cannot have any regrets and put everything into the matches. It's all about character, and at the moment we're a very nice bunch of players who are too easy to get beat."
Everton's remaining fixtures
April 9 - Man Utd (h)
April 20 - Leicester (h), live on Sky Sports
April 24 - Liverpool (a), live on Sky Sports
May 1 - Chelsea (h), live on Sky Sports
May 7 - Leicester (a)
May 10 - Watford (a)
May 15 - Brentford (h)
May 19 - Crystal Palace (h)
May 22 - Arsenal (a)