Manchester United revealed last week that it cost £19.6 million to sack Jose Mourinho and his coaches in December. If proof was ever needed that finding the right manager can be an expensive business, it was laid out in black and white, halfway down a news release about United's financial figures, under the section marked "exceptional items."

Chelsea, who face United in Monday's FA Cup fifth-round tie at Stamford Bridge (watch on ESPN+ on Monday at 2:30 p.m. ET), know all about sacking managers, too. When they dispensed with Mourinho during his second spell in charge in December 2015, the compensation package amounted to £8.3m, so the price of appointing the wrong man has clearly escalated over recent seasons. Yet, as the two clubs prepare to battle it out for a place in the FA Cup quarterfinals, managerial uncertainty continues to hang over both like a thick fog.

There are some rays of light beginning to shine through at United, with caretaker manager Ole Gunnar Solskjaer giving the club's hierarchy a different kind of problem in the sense that he might actually have become the best option for the job on a full-time basis. If he did get the permanent job, it would save them a reported £34m bill to prise Mauricio Pochettino from his Tottenham contract.

But at Chelsea, despite Thursday's 2-1 Europa League round of 32, first-leg victory over Malmo in Sweden, last summer's appointment of Maurizio Sarri is starting to look as though it is heading for the "expensive mistake" category. So Monday's cup tie, a repeat of last season's final which was won by Chelsea, has become a game that, while important for their respective hopes of silverware this season, is now all about two managers fighting for their future, albeit in wholly different scenarios.

Sarri needs a victory to silence his critics -- they include the club's supporters, who chanted, "You don't know what you're doing" during last month's 4-0 defeat at Bournemouth -- after a dismal run of results that has seen Chelsea drop to sixth position in the Premier League.

So far in 2019, Chelsea have played three league games away from Stamford Bridge and lost all three, conceding 12 goals in the process and scoring none. Sarri's refusal to compromise his football philosophy -- the so-called "Sarri-ball" -- has led to reports of players losing faith in his methods, a situation unlikely to have been helped by the 60-year-old twice criticising the commitment and motivation of his team in recent weeks.

Sarri is under fire already, in his first season as Chelsea manager, and heads into Monday's FA Cup clash needing a win to buy him some goodwill with his bosses and the fans. Richard Sellers/EMPICS/PA Images via Getty Images

In many ways, Sarri is replicating the mistakes made by Mourinho, both in his last spell at Chelsea and at United, by being inflexible with his tactics and too often pointing the finger of blame at his players. If he really is fighting for his future as Chelsea manager, he can only have himself to blame.

Yet in the opposing dugout on Monday, Solskjaer will be sending his team out (minus the injured Anthony Martial and Jesse Lingard) and hoping to see them bounce back from the first defeat of his temporary spell in charge, last Tuesday's 2-0 Champions League loss at home to Paris Saint-Germain.

Prior to that reverse, Solskjaer had worked an apparent miracle by guiding United to 10 wins out of 11 after inheriting a squad low on confidence and short on results from Mourinho in mid-December. The Norwegian was supposed to be little more than a short-term fix, a link to the club's glorious past under Sir Alex Ferguson and someone who would steady the ship until a more experienced, high-profile manager was appointed in the summer.

That may still happen but Solskjaer has made a compelling case to become United's permanent boss by avoiding the mistakes made by Mourinho and, in many aspects, Sarri. He's found a system that works, deploying the right players in the right positions in a 4-3-3 set-up and injecting pace in key areas. Within that, Solskjaer has focused on the talents of midfielder Paul Pogba and made his team more suited to the Frenchman's ability. It's in sharp contrast to Mourinho, who could not get the best from the £89m signing and by the end, regarded him as more of a problem than a solution.

Solskjaer has also given his players the freedom to express themselves and lightened the mood around United to the extent that the team is now playing with a smile on its face. Last week's defeat against PSG was perhaps a much-needed reality check, one that stemmed the hysteria around Solskjaer and reminded observers that neither he nor his team are yet the finished article. But there are enough signs of progress and positivity at United that Sarri desperately needs to see at Chelsea if he is to survive in the job.

Solskjaer is currently doing a wonderful job at Man United but defeat to PSG and pressure to rebound vs. Chelsea is causing doubt as to his bid for the permanent role. Jean Catuffe/Getty Images

Unlike Solskjaer, Sarri has been unable to make the 4-3-3 formation work, largely because of his refusal to operate with Jorginho at the hub of midfield despite the Italian's lack of pace or tenacity. It's a problem exacerbated by Sarri's decision to move N'Golo Kante away from his best position in order to accommodate Jorginho.

Chelsea's players have recently looked as though they are lost within Sarri's system and philosophy, especially away from home, and the manager has failed to get his best player -- Eden Hazard -- performing as impressively as Pogba is under Solskjaer. Hazard's reluctance to commit his future to Chelsea, opting instead to fuel speculation of a summer move to Real Madrid, has not helped Sarri, but the coach has equally shown little sign of being able to cajole the Belgian into displaying his best form. In many ways, Sarri is heading down the rabbit hole that cost Mourinho his last two jobs, while Solskjaer is doing everything possible to make sure he does precisely the opposite.

Ultimately, neither Sarri nor Solskjaer may survive at the helm to take charge of their clubs next season, but only one of them -- Solskjaer -- is giving himself a chance of holding onto his job. If Sarri continues on his current path at Chelsea, the club will need to prepare for another costly compensation package.