Speculation over Godfrey's future at Goodison Park has been rife for some time, with the 26-year-old's contract due to expire in 12 months' time.
Godfrey joined the Toffees from Norwich City for a fee rising to £25m in October 2020 and has since made 93 first-team appearances across all competitions.
The versatile defender initially struggled for game time under manager Sean Dyche last season, but he eventually established himself as a first-team regular during the latter stages of 2023-24.
Indeed, Godfrey started in 12 of Everton's final 17 Premier League matches as Dyche steered his side away from the relegation zone and up to 15th place.
Godfrey to undergo Atalanta medical ahead of £10m move
Amid concerns over the prospect of breaching the Premier League's Profit and Sustainability Rules, Everton are under pressure to sell players before the June 30 deadline.
Godfrey is one name who has attracted interest from a number of clubs both in England and abroad, and it now appears that Atalanta have moved to the front of the queue for his signature.
According to multiple reports, including one from BBC Sport, Atalanta have agreed a deal in the region of £10m with Everton to sign Godfrey, who saw a move to La Dea fall through in January.
Godfrey is expected to travel to Milan on Friday for a medical with last season's Europa League winners, who will be competing in the 2024-25 Champions League.
Fellow Serie A outfit AC Milan and Bundesliga side Borussia Dortmund have recently been credited with an interest in Godfrey, while Ligue 1 club Lyon have allegedly tabled a £12.7m bid.
However, it seems that Godfrey's preference is to join Atalanta, with experienced manager Gian Piero Gasperini known to be an admirer of the defender.
Should Godfrey complete his move to La Dea, he would link up with former Everton winger Ademola Lookman, who has elevated his game to new heights since making the switch to Italy.
The money generated by Everton from the sale of Godfrey could go towards their signing of striker Iliman Ndiaye, who has allegedly completed his medical ahead of a £20m move from Marseille.
The Toffees have already been busy in the summer transfer window, signing midfielder Tim Iroegbunam from Aston Villa for a reported £9m, while Jack Harrison has returned on loan from Leeds United for the 2024-25 season.
Further outgoings could also be on the cards, with the likes of Jarrad Branthwaite and Amadou Onana being linked with following Lewis Dobbin - who has joined Aston Villa - out the exit door.