With just two days to go until their opening Premier League fixture of the season against Chelsea, the Toffees have made three first-team additions.
Before the recent signings of Ruben Vinagre and Dwight McNeil, boss Frank Lampard strengthened his backline with the acquisition of James Tarkowski.
However, Lampard is said to want to bring more more senior figures to Goodison Park, a desire which will seemingly lead to an approach being made for Wolves' captain.
According to Sky Sports News, the Merseyside outfit are ready to hand the 29-year-old an opportunity to return to Merseyside.
Coady was born in nearby St Helens and spent nine years at Liverpool, making just two first-team appearances before departing Anfield in 2014.
Since then, Coady has established himself as an influential figure in the centre of Wolves' back three, making a total of 317 appearances during seven years at Molineux.
However, while Coady featured in every Premier League fixture during 2021-22, the England international is expected to start on the substitutes' bench against Leeds United at the weekend.
Bruno Lage has made the decision to switch to a back four with new arrival Nathan Collins and Max Kilman currently being regarded as first choice.
While the report states that Wolves would prefer to retain the services of their leader, a departure cannot be ruled out with Coady wanting to push for a place in Gareth Southgate's World Cup squad.
With Coady having three years remaining on his contract, it is unclear whether Wolves would be open to a permanent sale or a loan exit for a season.
Everton have been linked with a number of players with Wolves connections this summer, seemingly a consequence of their former director of football Kevin Thelwell now working alongside Lampard.
However, while former Wolves man Vinagre has already signed for Everton, Leander Dendoncker appears likely to stay in the West Midlands and Nottingham Forest are favourites to sign Morgan Gibbs-White if they meet Wolves' asking price.