Randolph joined West Ham from Middlesbrough in the winter of 2020 and has managed only eleven appearances for the Hammers since joining.
The experienced 35-year-old goalkeeper is currently behind Lukasz Fabianski and Alphonse Areola in the pecking order.
West Ham have also recalled young goalkeeper Joseph Anang, who was on loan at League One side Derby County.
Randolph’s contract with the Hammers will run out at the end of June and Bournemouth are interested in the 35-year-old.
It has been claimed that the Cherries are holding talks with West Ham to bring the player to the Vitality Stadium on a permanent move in the current transfer window.
Bournemouth, who are currently in the bottom half of the table, wants to provide competition and cover for Mark Travers and Neto in goal.
The Hammers are well stocked in their goalkeeping department and might be willing to cash in on Randolph in January.