Both sides have an opportunity to progress into the top five on the Premier League table this weekend.
With Liverpool and Arsenal invariably stuck in a period of slippage, and both sides facing each other this weekend, there's an opportunity for Everton and Manchester United to pounce for European football.
After a sluggish start to the season, United have staged an effective recovery.
Since October, Jose Mourinho's side have not lost a Premier League tie, which is the longest run without a defeat in the league this season.
Winning the EFL Cup final last weekend, albeit on the back of an unfairly disallowed goal for Southampton, has injected a new sense of confidence in Jose Mourinho's charges.
Meanwhile, Everton can realistically target a qualification spot for Europa League football next season.
Man United v Bournemouth: Saturday March 4th 12.30pm
The records favour United in this fixture, with the former winning all five previous meetings at home. Additionally, Bournemouth are just four points above the relegation zone, having lost their last four Premier League games ahead of this fixture.
A defeat against United would mark the first time they suffered five consecutive league defeats since 2013.
Henrikh Mkhitaryan is still unavailable for selection due to a hamstring injury, but Phil Jones has been declared fit to play following a month out with a foot injury.
If Zlatan Ibrahimovic can continue his goal-poaching form, this should be a routine win for United, which would see them temporarily move up the table, at least until the 5.30pm kick-off between Liverpool and Arsenal.
Not content to settle for Europa League football anymore, United will be eager to restore their Champions League status again.
Spurs v Everton: Sunday March 5th 1.30pm
Everton face a stiffer assignment this weekend, against the in-form Tottenham Hotspur, who devoured Stoke City last weekend.
Facing them at White Hart Lane heightens the difficulty involved, given Spurs' unbeaten home record in the Premier League.
Everton could be in for a potential reprieve however. Harry Kane, who claimed a hat-trick last weekend, is being monitored after colliding with a goal post in that 4-0 rout.
Kane along with Toby Alderweireld and Jan Vertonghen will all undergo fitness assessments ahead of the meeting with Everton.
Spurs boss Mauricio Pochettino told Sky Sports that while those players are doubts for Sunday, he is hopeful they will get the clearance to play.
Should Kane be forced to withdraw from selection, Everton's chances of clinching a win would significantly increase.
But irrespective of Kane's likelihood of featuring in the game, Koeman's men are are nine games unbeaten in the league and key striker Romelu Lukaku is in devastating form.
He's hit 17 league goals so far this season, and is just one short of his career best of 18, which he set last year.
Everton are currently five points behind Liverpool, and if their neighbours slip up against Arsenal, they would take a significant step towards clinching that Europa League spot.