David Unsworth will likely take temporary charge whilst Farhad Moshiri and Bill Kenwright search for the man to replace Koeman on the Everton touchline.
We’ve drawn up a list of five somewhat realistic potential candidates the Blues could attract, ranging from well-known names across Europe to a few current Premier League managers who may be being considered to step into the Goodison Park role.
The former Borussia Dortmund boss is currently out of a job since parting ways with the German club in May.
In the past, he has stated that he wants to manage in the Premier League but was not targeted by any clubs before joining Dortmund in June of 2015. There had been reports that he was being considered for the Newcastle United job when Alan Pardew left to join Crystal Palace.
The Bavarian-born boss has already reportedly rejected a chance to take over at Leicester City, favouring his chances of waiting for a more established club to come along elsewhere in Europe.
Tuchel has a set and clear system that could adapt well to Goodison Park. His high-intensity game is less gegenpressing and more counter-attacking with pace utilising wing backs higher up the pitch.
Whilst his system in attack can be a little predictable when an opposing team allows Tuchel’s side to play on the ball and retain plenty of possession, the style of playing on the last defender’s shoulder and playing plenty of through balls could suit the current Everton team down to a tee.
Tuchel may be tough to get but the Blues at least have to ask the question of the German boss.
The Portuguese boss nearly completed the impossible last season, as he almost guided Hull City to Premier League safety. He came within a matter of inches of completing a near miracle but ultimately, the damage had already been done before he got there.
Now in charge at Vicarage Road, he has the Hornets playing eye-catching football that is leading to results. His side were unlucky not to beat Chelsea on Saturday afternoon but missed a number of key chances that would have changed the result.
With his side playing so well, it’s unlikely the 40-year-old boss would swap Watford for Merseyside at the minute but Everton can only inquire and test his hand.
Ancelotti is perhaps the most ambitious shout to take over as the new Everton manager but the Blues are likely to at least ask the question.
The Italian boss is out of work following his departure from Bayern Munich earlier this month and has already stated his desire to one day work in the Premier League again.
The worry surrounding the 58-year-old boss is that he is perhaps to similar to Koeman in that he isn’t an Evertonian and doesn’t ‘get’ the club, the way fans want a manager to.
That doesn’t always work however, just ask Roberto Martinez.
Ancelotti has never really managed a club in free fall, that’s needs saving and he’ll probably wait it out for a better opportunity to present itself later in the season.
Moshiri and his men will make the call but it’s unlikely the Italian answers.
Sean Dyche has already been tipped as the favourite to take over at Goodison Park and whilst he wouldn’t necessarily bring the excitement favour some fans may crave from a new boss, he could bring a certain amount of stability.
Yet, the former Watford man seems set at Burnley. His current side are playing some of their best football in a long time and sit comfortably in the top half of the Premier League table.
Dyche draws comparisons to former Everton boss David Moyes, in the sense that Burnley is perhaps a ceiling and breaking through, with ambition, may not be the greatest move in the world.
There are also questions about his ability to potentially work with ‘big’ players such as Wayne Rooney. The 46-year-old has worked with Michael Keane in the past and the defender would likely serve as a gateway into the Everton squad.
Eddie Howe is the biggest dark horse of the five listed candidates but he ticks plenty of the Goodison Park needs and wants boxes. For starters, he’s a young manager who, for the most part, plays an attractive brand of football that gets results home and away.
He’s also a lifelong Everton fan and would immediately tick the box that concerns a manager who understands and gets the club.
Whether or not he’s actually in the thoughts of the Everton decision makers is another question.
Yet, the 39-year-old seems settled at AFC Bournemouth despite being linked with jobs elsewhere when vacancies come about.
Howe is most certainly the least likeliest of the list but his connection to club puts him with a shout, if he’s being considered.