The 27-year-old penned a seven-year contract with the Hammers last year, and an impressive 2023-24 campaign saw him manage 20 goals and 10 assists in 44 appearances in all competitions.
Bowen is currently with the England squad at Euro 2024, and he featured off the bench in their opening two games at the competition against Serbia and Denmark.
Newcastle are said to be keen to sign the forward this summer, but according to Football Insider, West Ham have made it clear that he will not be allowed to leave for under £100m.
As a result, a summer departure is highly unlikely, with the Magpies now expected to move onto other targets.
Since arriving at the London Stadium from Hull City in January 2020, Bowen has represented the Hammers on 202 occasions in all competitions, scoring 60 goals and registering 39 assists in the process.
Middlesbrough 'keen' on deal for Swift
Elsewhere, according to Football Insider, Middlesbrough are keen to sign West Bromwich Albion midfielder John Swift during this summer's transfer window.
The 29-year-old has another year left to run on his contract at West Brom, and he made 41 appearances for the Baggies during the 2023-24 campaign, scoring nine goals and registering one assist in the process.
West Brom are believed to be open to letting the midfielder leave for the right price this summer, though, and Middlesbrough are allegedly keen on his signature.
The report claims that Boro view him as a player capable of helping them challenge for a return to the Premier League during the 2024-25 campaign.
Swift made the move to the Baggies from Reading in 2022, and he has represented his current side on 87 occasions in all competitions.
Swansea 'fail' with offer for St Johnstone's Sidibeh
Meanwhile, according to The Courier, Swansea City have seen an opening bid for St Johnstone forward Adama Sidibeh quickly turned down by the Scottish outfit.
The 26-year-old made the move to St Johnstone from English non-league outfit Warrington Rylands in January, and he ended last season with five goals for the club.
Football Insider had reported that Swansea had made an offer for a player who has also been linked with Burnley, Middlesbrough and Derby County this summer.
However, it is alleged that St Johnstone did not even consider the bid from Swansea, as it fell considerably short of their valuation of the attacker.
Sidibeh, who scored on his international debut for The Gambia, has a contract with his current club until May 2026, and he is expected to report for pre-season training this week.