It shouldn’t be a debate. When Chelsea conduct their end-of-season review this coming week, it would be ridiculous if they convince themselves that the right call would be to get rid of Mauricio Pochettino and begin yet another search for a head coach.

The good news is that prominent figures inside Stamford Bridge are backing Pochettino. Why change now? Why start over when the players want the manager to stay? Why not recognise that Pochettino, who has dealt with a massive injury list, made sense of a dizzying transfer strategy and built a team that stand close securing European football before hosting Bournemouth on Sunday afternoon?

Only an impatient person would swing the axe. However, a few weeks ago there was a sense that Chelsea were planning for a split with Pochettino, even with replacements thin on the ground. Hopes of Champions League football were long gone and some figures at Chelsea, where more than £1bn has been spent under the ownership of Clearlake Capital and Todd Boehly, wanted Pochettino fired after April’s 5-0 defeat by Arsenal.

That he survived was ultimately at the insistence of Clearlake, the private equity fund managed by Behdad Eghbali and José E Feliciano. Stability is vital. Although Eghbali is understood to have had reservations about Pochettino from the start, the emotion was taken out of it and the stirring response to the humiliation against Arsenal has shifted the dynamic.

Chelsea, who rose to sixth after beating Brighton in midweek, have four wins and one hard-earned 2-2 draw with Aston Villa from their past five games. Losing the Carabao Cup final to Liverpool’s kids was poor but Gary Neville’s “Blue billion-pound bottle jobs” jibe no longer feels quite as cutting.

It is, though, still possible to detect some ambivalence towards Pochettino. Members of the ownership team flew in from the US morning – they went to Manchester to watch Chelsea’s women attempt to clinch the WSL title at Old Trafford – and are still undecided on whether to keep him before the review. They need to gauge Pochettino’s mood, his willingness to adhere to their way of working, although they think he will be happy if they ask him to stay. That they are drawing up a list of potential replacements should talks end in the 52-year-old leaving indicates a split is possible.

It is suggested Pochettino took too long to settle on the right tactical formula and there is concern his training methods may have contributed to Chelsea’s injury problems. Attacking and defensive set pieces have also been a problem.

The upturn in form is seen as evidence that the co-sporting directors, Laurence Stewart and Paul Winstanley, and the co-director of recruitment and talent, Joe Shields, deserve to be hailed for their sterling work in the transfer market.

The head coach needs to be willing to thrive in this “collaborative” environment. It took Pochettino a while to accept the need for a set-piece coach, the club taking Bernardo Cueva from Brentford.

“This is not my team, this is Chelsea’s team,” Pochettino said after the Brighton game. He has not made his own signings. Going into the season with so many young players was not his idea. He has built from scratch in the toughest league in the world.

In that context he has done his job, all while the club’s internal power dynamics rumble on. Who sets Chelsea’s culture? Is there ­unanimity over the long-term vision? Boehly, the chairman, has started to talk about the importance of patience. But Eghbali is believed to be highly influential. There is a lot of chatter and any decision to change manager would need to be signed off by Boehly and Clearlake. At the moment, the feeling is that the manager stays.

Understandably, the speculation has unsettled Pochettino. Chelsea, who are fourth in the form table since Christmas, are moving in the right direction. His recent talk about quitting is not a good development. Pochettino has been flexing his muscles. He may sense that Chelsea need him more than he needs them. They will need to decide whether missing out on the initial target of a top-four finish is acceptable. The view is that this is a top-four squad.

Pochettino will go into the review with his own views. He wants more control over signings. But there could be tension if Chelsea press ahead with plans to sell Conor Gallagher and Trevoh Chalobah. That would not help Pochettino.

He has not been perfect. Shipping late equalisers against Burnley and Sheffield United? Not great. Thirteen games without a clean sheet? Talk about disgracing José Mourinho’s legacy. Chelsea have lacked control for much of the season. Games have been chaotic, with leads squandered, horrendous goals conceded and the team often ­imploding shortly after half-time. Pochettino fumed at his players for not trying hard enough against Burnley.

Yet any honest assessment of Pochettino’s work would also show strong performances against the top sides and they should have won their FA Cup semi-final against Manchester City. It would acknowledge how he has improved Cole Palmer, Malo Gusto, Nicolas Jackson, Noni Madueke, Marc Cucurella and Gallagher. Out of the chaos, glimpses of a proper team are emerging. Moisés Caicedo, the £115m midfielder, is thriving now that he does not have to carry Enzo Fernández, who played with a hernia for eight months before going for surgery.

As for criticism of Pochettino’s game management, it is worth pointing out that Chelsea have earned 18 points thanks to goals in the final 15 minutes. A total of 62 goals conceded, the second most in the top half, needs to improve but is to be expected given all the chopping and changing. The late shows are proof of a team with good fitness levels and a strong attitude and it is easier to make decisive substitutions when Reece James, Raheem Sterling and Christopher Nkunku are available to come off the bench.

The injuries should not be ignored. James, the captain, has missed most of the season. Nkunku, who scored after coming on against Brighton, has started two games since his £53m move from RB Leipzig. His lengthy absences would have been a blow for any manager.

Pochettino has constantly had to put out fires. Now he is building momentum. It is not the time for more upheaval.