Koeman’s men have won only two of their last 15 away games and taking on Paul Clement’s relegation battling Swans won’t present an easy opportunity to break that run.
One thing the Dutchman’s team can take solace in is that Everton have never lost a league match away to the Swans but they’ve never faced the Welsh side in this position before.
The last time the two sides met, Bob Bradley was in charge for Swansea. The American boss narrowly missed out on his first win as Swansea boss as a 90th minute Seamus Coleman looping header secured a point for Everton.
Gylfi Sigurdsson put the Swans ahead just before half-time with a goal from the penalty spot but the visitors were unable to hold on to their lead.
That lacklustre draw came off the back of a disappointing result for Everton against Chelsea but that is the only similarity Koeman’s side will be pointing to this time around.
The game will also see the return of Ashley Williams to the Liberty Stadium for the first time since his move to Everton.
In focus: Everton's troubles on the road
It’s well documented how well Everton have performed at Goodison Park since the turn of the year. The 3-0 defeat to Chelsea last week was the first loss since the Merseyside Derby defeat to Liverpool and only the second Premier League loss at Goodison Park all season.
On the road, it’s been quite the opposite story for the Blues.
Despite performing well at times, they have struggled to turn those performances into wins away from Merseyside.
There may not be a sole reason for that but whatever it may be, has to be figured out in time for next season, when Koeman’s side will look to mount a Champions League qualification bid on the Premier League front whilst balancing the pressures of the Europa League campaign.
Players have to step up away from the comfort of Goodison Park too. Only one of Romelu Lukaku's 14 goals this year has come away from home.
The Belgian forward may be presented with more space and support whilst at home but on the road, he has to create opportunities for himself and can find regularly himself isolated against a tough defensive back-line.
Whatever the problem is, Everton have to figure it out and quick.
A look at Swansea City
Swansea City have had a rocky season by their standards during their time in the Premier League but have seemingly found a bit of stability under Clement.
They sit 18th in the Premier League table, just two points away from climbing out of the drop zone, provided results go their way this weekend.
It took the Swans until the third week of the season to pick up their first win but after that followed a barren spell as it took under the end of November to win their second game. In that time, Francesco Guidolin was sacked and replaced by Bob Bradley. The American lasted 85 days before being dismissed himself.
The one shining star for the Welsh side this season has been the form of their Icelandic talisman Gylfi Sigurdsson.
Sigurdsson has been linked with a summer move to Everton but it will take close to £30 million to see him depart, although relegation from the Premier League may alter that line of thinking.
The 27-year-old has scored in three of the last six meetings in all competitions between the two sides and will once again be the danger man for Swansea this time out.
Swansea: Fabianski, Naughton, Fernandez, Mawson, Olsson, Britton, Fer, Carroll, Sigurdsson, Ayew and Llorente.
Everton: Stekelenburg, Baines, Jagielka, Williams, Holgate, Gueye, Davies, Barkley, Mirallas, Lookman and Lukaku.
Match Day Stats:
1. Everton have lost their first game in May in each of the last 3 seasons.
2. Swansea could secure their first back-to-back home wins since May 2016
3. Everton have not lost a league match in Wales since 1956, losing 1-0 to Cardiff.