Stoke were relegated last weekend and Allen is one of the few players who might remain in the Premier League next season. The Telegraph reports that an unusual clause in his contract means that one of the big six can sign him for a fixed fee of £25m.
The only member of the top six not included in this clause is Liverpool, the team from whom Allen joined Stoke for £13m in 2014. If another club wants to sign Allen, Stoke have no contractual obligation to sell regardless of price.
West Ham had a bid of about £25m rejected in January but it remains to be seen whether they will renew their interest this summer. Stoke intend to take a hardline stance but their relegation could force them to sell at a lower price than originally intended.
If the Hammers do decide to go back in for Allen, they may face opposition from other clubs including Newcastle, Swansea and Sevilla, all of whom have been linked with the 34-year-old Welshman.
Swansea seem unlikely to sign Allen, after they too were relegated to the Championship after failing to manufacture the correct set of final day results.
However, that move may hold sentimental value for Allen, as he started his career at the South Wales club and made 150 appearances for the Swans before joining Liverpool in 2012.
Allen never really found his feet at Anfield but rediscovered his touch at Stoke, enjoying the most prolific season of his career last year with six goals.
However, he scored just two goals this season as the Potters were relegated with a game to spare.