Everton have applied to enter the Intertoto Cup.
The Toffees are currently fourth in the Premier League, which would be good enough to earn them qualification for the preliminary rounds of next season's Champions League.
Three further teams qualify for the UEFA Cup, with the next highest-ranked side eligible to enter the pre-season Intertoto Cup, which offers an alternative route into the UEFA Cup.
Aston Villa, Blackburn and Manchester City have also applied for entry to the competition.
Everton are still in this season's UEFA Cup, and will face Italian side Fiorentina in the last 16.
Everton chief executive Keith Wyness told: 'Clearly European qualification through our league position or via the UEFA Cup is our main priority.
'However because of the deadline for Intertoto Cup applications, it would be remiss of us not to put our name forward.'