Randolph joined West Ham in the summer of 2015 on a free transfer after leaving Birmingham City at the end of the 2014-15 season.
The Republic of Ireland international is the second-choice goalkeeper behind Adrian at the Hammers.
According to the British tabloid, West Ham manager Slaven Bilic will allow Randolph to leave the London club this summer as long as they get a transfer fee of around £3 million.
The former Motherwell and Birmingham goalkeeper has two years left on his current £22,000-a-week deal with the option of a further year at West Ham, according to The Sun.
Randolph kept one clean sheet in four appearances for the Republic of Ireland at the Euro 2016 finals in France, making 3.25 saves per game and 2.60 saves per goal on average.
During the 2015-16 campaign, the goalkeeper played in just six Premier League matches for West Ham, keeping two clean sheets in the process.