After substantial investment in new recruits during the off-season, Everton's expectations were raised but the performances have been so poor that Koeman may well have departed even if the goal was simply to repeat last season's seventh place.
The Merseyside club were beaten 5-2 at home by Arsenal on Sunday, following a 2-1 home loss at Goodison Park to Lyon in the Europa League.
Those defeats might have been tolerated had they not followed the disappointment of a 1-0 home loss to Burnley and a September which included 3-0 losses to Tottenham Hotspur and Atalanta and a 4-0 drubbing at Manchester United.
For the truth is that far from progressing this season, Everton have taken a dramatic step backwards.
Koeman joined after in 2016 after guiding Southampton to seventh and sixth place in his two years at St Mary's.
Before coming to England, Koeman finished in the top three in the Dutch league in all three of his seasons with Feyenoord. He had previously won the Eredivisie with Ajax and PSV Eindhoven
The only major blemish on the 54-year-old's CV had been his brief spell at Valencia in Spain where he lasted 22 games and left the club in 16th place.
That pedigree, combined with a willingness to blood young players, made Koeman an excellent choice for Everton as they looked to progress as a club while bringing through a talented generation from their development squad.
But the latest transfer dealings, in which the club spent 149 million pounds but also sold top scorer Romelu Lukaku to Manchester United for 75 million, undid the solid start the Dutchman had made in his first season.
The club did not spend any of their money on directly replacing Lukaku with a proven spearhead likely to bag 20 goals a season - instead spreading it around as they brought in nine new players.
The mistakes in the market were all too evident against Arsenal, the line-up overloaded with attacking midfielders in Gylfi Sigurdsson, Nikola Vlasic and Wayne Rooney and only Idrissa Gueye, sent off in the second half, capable of defensive midfield work.
Up front, young striker Dominic Calvert-Lewin was left to lead the line alone, a role unsuited to a promising but still developing 20-year-old.
Another summer recruit, attacking midfielder Davy Klaassen who was signed from Ajax for 24 million pounds, sat on the bench having failed to impress.
A solid midfield organiser and a real centre-forward, were sorely missing from the formation and whether it was Koeman who was primarily responsible for the recruitment or Director of Football Steve Walsh, the muddled dealings have been at the heart of Everton's problems.
Everton face the tough task of finding someone who can sort out the squad, discard unwanted players and fill the obvious gaps - all while ensuring they climb away from the relegation zone.
(Reporting by Simon Evans, editing by Ed Osmond)
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