These sides met in the third round of this competition two seasons ago, with the Toffees running out 5-2 victors.
Match preview
After almost losing their League One status last season, with Gillingham relegated via goal difference at their expense, Fleetwood are hoping for a more stable season under their new manager Scott Brown.
Following a beneficial year spent as Aberdeen's assistant, the former Celtic midfielder has stepped into his first managerial role with reasonable aplomb so far, taking six points from five matches while beating Championship side Wigan Athletic to set up an intriguing second-round tie against Everton.
The Cod Army certainly look tougher to beat than last season, when they shipped an eye-watering 82 goals in 46 matches. Indeed, two successive 0-0 draws heading into Tuesday's cup tie perhaps shows where Brown's priorities have lied, at least in the early stages of his tenure.
Likewise, a cup run is unlikely to be high on the agenda for a club many expected to struggle once again this season, but whenever a Premier League team enters town it is always an occasion which no manager or player will want to let pass by without giving their all in.
Everton, of course, only continued their ever-present Premier League status with one match to spare last season, after a tumultuous season under the managemtn Rafael Benitez and Frank Lampard.
The former England midfielder may have feared the worst after Brennan Johnson broke the deadlock for Nottingham Forest at Goodison Park in the 81st minute on Saturday, with the Toffees staring down the barrel at three league defeats to open the season.
However, Demarai Gray spared his manager's blushes with only two minutes remaining to potentially kick-start his side's season. With Dominic Calvert-Lewin out injured once again, though, Lampard will surely be determined to attract a higher calibre of striker than he currently has at his disposal.
Having failed to win a trophy since 1995, Everton's fans will likely be baying for their manager to pick a strong team at Fleetwood on Tuesday, but with Premier League survival surely taking priority this campaign, the 44-year-old has a major job on his hands to ensure his team avoid a damaging upset on Tuesday.
Fleetwood Town EFL Cup form:
Fleetwood Town form (all competitions):
Everton form (all competitions):
Team News
Fleetwood will remain without central defender Darnell Johnson, who continues his rehabilitation from an Achilles tendon rupture.
Brown picked a fairly strong team in the previous round's victory over Wigan, so he is unlikely to make too many changes from the weekend's decent draw against Derby County.
Joe Garner, Cian Hayes and Carl Johnston will all hope to come into the attack having been used from the bench on Saturday, with Hayes perhaps likely to win that battle.
Everton, meanwhile, will travel without Calvert-Lewin (knee), Yerry Mina (ankle) and Abdoulaye Doucoure (muscle), with the trio likely to be at least a few weeks away from returning to first-team action.
Ben Godfrey (fibula fracture) and Andros Townsend (ACL) are long-term absentees, but Andre Gomes could be a part of the squad after his recent knock.
Lampard will almost certainly freshen thing up more than his counterpart, with Seamus Coleman set to captain the side having lost his place to Nathan Patterson in the early weeks of the campaign. Allan could partner Amadou Onana in midfield, with Michael Keane, Dwight McNeil, Dele Alli and Ruben Vinagre all handed crucial match fitness.
Fleetwood Town possible starting lineup:
Lynch; Rooney, Earl, Nsiala, Andrew; Sarpong-Wiredu, Vela, Macadam, Batty; Hayes, Garner
Everton possible starting lineup:
Begovic; Holgate, Coady, Keane; Coleman, Allan, Onana, Vinagre; McNeil, Alli; Rondon
We say: Fleetwood Town 0-1 Everton
With both teams playing safety-first football in the opening weeks of the campaign, it is hard to see too many goals being scored at Highbury Stadium on Tuesday.
Despite being likely to make several changes, the Toffees should be able to keep their League One opponents at arms length and marginally progress to the next round.