After a troubled season where the Toffees struggled in front of goal, Sean Dyche made his feelings clear following the end of the campaign about adding firepower to the squad.
Neal Maupay scored just once during 2022-23 but has played in both of Everton's pre-season friendlies so far against Stade Nyonnais and Wigan Athletic.
First-choice striker Dominic Calvert-Lewin missed the final game of the season against Bournemouth and is currently still on the road back to full fitness.
It is believed Dyche was hoping to add at least two attackers to his side ahead of the start of the season, and the club completed the loan signing of Arnaut Danjuma over the weekend.
Fabrizio Romano now claims that Everton are in the fight for Toure, but face stiff competition from Atalanta.
Atalanta have become renowned as a club where attackers can thrive under the stewardship of Gian Piero Gasperini, whose attacking mentality has often seen La Dea top the Serie A scoring charts.
The Bergamo-based club are also likely to have stronger buying power than Everton, if a deal for Rasmus Hojlund to join Manchester United goes through.
Toure has a release clause of €40m (£34m) at Almeria, and the club are believed to be holding out for a bid that meets the clause.
Everton's restricted spending means they are likely going to make a bid in instalments, while Atalanta could pay a bigger portion up front should Hojlund bring in a substantial sum of money.
Almeria already appear resigned to losing Toure this summer, as Romano also states that they have opened negotiations to sign Ibrahima Kone from Lorient.
Toure arrived from fellow Ligue 1 club Reims last summer for €8m (£7m), and bringing in a fee five times higher just 12 months later will allow Almeria to afford a suitable replacement.
Should Everton miss out on Toure, then Kelechi Iheanacho has allegedly been touted as a potential alternative.
FootballTransfers claims that the Nigerian, who was relegated with Leicester City last season, is of interest to the Toffees, but only as an alternative.
Iheanacho scored eight goals for the Foxes last season, but his game time was restricted due to injury and the battle for a starting spot with Jamie Vardy and Patson Daka.