West Ham are in talks with Chelsea over their Italy full-back Emerson Palmieri.
Injuries to new signing Nayef Aguerd and experienced duo Craig Dawson and Angelo Ogbonna have forced Moyes to use Ben Johnson in central defence so far this season alongside Kurt Zouma.
West Ham are also understood to be looking at Paris St-Germain's German defender Thilo Kehrer, 25.
Emerson spent last season on loan at Lyon from Chelsea, making 29 league appearances for the French side.
However, he has little future at Stamford Bridge following the arrival of Marc Cucurella from Brighton, even though Emerson still has two years left on his current contract.