Sunderland midfielder Jack Rodwell has suffered with a series of injury problems in recent seasons.
Alexis Sanchez has shown he is busy working on his fitness.
Brendan Galloway agreed a contract extension with Everton.
The ex-Lyon boss has already started identifying potential targets ahead of talks with chairman Randy Lerner.
The Hammers are currently seventh in the table after a strong start under Slaven Bilic.
The Newcastle United winger is nearing a return to full fitness.
Leicester City and Chelsea are set to meet on Monday evening.
The left-back has been in good form for West Ham once again this season.
Sunderland wanted to sign Aiden McGeady during the summer.
The Ghanaian international suffered a serious knee injury in June.