The Arsenal academy graduate has scored three goals and provided eight assists in 132 appearances for the club, but in the last couple of seasons, he has been sent out on loan for spells with West Bromwich Albion and Roma.
Maitland-Niles is not part of Mikel Arteta's plans, and as a result, Arsenal are currently looking to offload the Englishman before the transfer window closes.
According to the Standard, Arsenal have offered West Ham the chance to sign the versatile player, but the Hammers are currently focusing on other targets.
West Ham have been linked with Club Brugge captain Hans Vanaken and Chelsea midfielder Conor Gallagher, and the Hammers would not consider a move for Maitland-Niles until later in the transfer window, when they could look to agree a loan deal.
Rather than a loan departure, Arsenal are keen to secure a permanent transfer for the 24-year-old, but they are yet to receive any serious offers.