The 26-year-old has barely featured under Sean Dyche this season, slipping down the pecking order to fourth-choice in the centre of defence.
Godfrey has started just twice this season - against League Two Doncaster Rovers in the EFL Cup, and at left-back against Burnley during a selection crisis for Everton.
With Milan on the hunt for more defensive reinforcements this month, Calciomercato claim a move for Godfrey is one of the avenues the Rossoneri are considering.
Milan have shopped in the Premier League for a defender before, when they bought Fikayo Tomori from Chelsea back in 2021, and another Englishman could soon be on his way to San Siro, after Ruben Loftus-Cheek also made the switch in the summer.
An injury to Tomori is one of many that Stefano Pioli is currently dealing with though, as Pierre Kalulu and Malick Thiaw are also sidelined.
The experienced Simon Kjaer has also missed a large period of the season, with offensive left-back Theo Hernandez often being forced into a central defensive role.
Jan-Carlo Simic has been fast-tracked into the first team and was given his debut towards the end of 2023, while Matteo Gabbia has been recalled from his loan at Villarreal to help manage the mounting injuries, and has instantly become a regular.
A move to San Siro could give Godfrey a new lease of life, with his Everton career currently fizzling out.
With just 18 months left on his contract at Goodison Park, the ex-Norwich City man evidently has no future under Dyche, especially while James Tarkowski and Jarrad Branthwaite continue to impress.
Michael Keane is also the preferred option when suspension, injury, or a change in formation comes about, meaning Godfrey has been an unused substitute in every game except for one this season when he has not been given a rare start.
Lilian Brassier of Brest has been another name touted to join Milan, but with heavy interest in the player across Europe, a bidding war could prevent the Serie A club from acquiring the promising youngster.
Godfrey's versatility is believed to be of interest to Milan too, considering he has played all across the backline during his spell at Everton.
Even the FA Cup has not provided Godfrey with any game time, and should he sit out Everton's fourth round tie with Luton Town on Saturday, that could push him closer to the exit.