Bowen netted nine Premier League goals as the Hammers slipped out of the top-flight in the final weeks of the 2025/26 campaign and West Ham now face a huge call on their captain's future.
With the 29-year-old under contract until 2030, West Ham are safeguarded from having to sell him, but Bowen's own personal desire to keep playing at the highest level could force an exit compromise between both parties.
Everton transfer correspondent Alan Nixon has confirmed Moyes' interest in signing Bowen, with the pair sharing four and half seasons together at the London Stadium, after Moyes made him his first signing at the club back in January 2020.
The Toffees are open to matching Bowen's wages at West Ham, but the two clubs are still some distance apart in their valuations of the former Hull City man, with Moyes hoping to secure a deal for around £20M - but the Hammers hierarchy want closer to £25M.
If Bowen does move on this summer he will miss the chance to break West Ham's Premier League goal record (65) as he currently sits three behind Michail Antonio (68)