Stoke are currently fighting to stay in England's top division, and are five points adrift of safety. With only three games remaining for The Potters, they look like likely candidates to face the drop.
If Stoke do fail to climb out of the bottom three, they could struggle to keep hold of some of their players, with Allen and Butland both likely to be in demand.
The Hammers have seemingly already anticipated this situation, and are thought to be lining up a £40m double swoop for the pair. Although the London club are not yet safe from the drop themselves, they are six points clear of 18th placed Southampton and are expected to secure another year in the Premier League.
Welsh midfielder Allen was linked with a move to the London Stadium in January, with Hammers' boss David Moyes seemingly interested in the former Liverpool star as he bids to improve his squad in that department.
And with Joe Hart's future uncertain, West Ham are expected to prioritise bringing in a new addition between the sticks.
West Ham fans have taken to social media to express their views on the proposed deal, and it seems to have split opinions.
Butland and Allen would improve us massively hope we can get one of them— Joe (@Evxrest) April 22, 2018
Would happily take Joe Allen and Jack Butland next season 👏🏼👏🏼— Sam Harding (@samharding_93) April 23, 2018
Really?!?!— BobbyBelcher (@BobbyBelcher) April 22, 2018
Butland has been linked with some of the Premier League's biggest clubs, with Arsenal and Chelsea both thought to have shown interest in the England international. The 25-year-old stopper would be a great addition, but Stoke are likely to demand a high fee for their keeper.
Stoke's remaining games are against Liverpool, Crystal Palace and Swansea, and may have to win all three matches if they want to avoid the drop.