Football.london report Moyes was keeping an eye on Ryan Fredericks, Tom Cairney and Aleksandar Mitrovic.
The latter is on loan from Newcastle and has scored a miraculous eight goals from as many appearances since leaving St. James' Park in January.
Fredericks and Cairney have been both long term targets for the Hammers.
A Tottenham youth product, 25-year-old Fredericks operates as a right-back and has made 90 league appearances since leaving Spurs for the Cottagers in 2015.
Midfielder Cairney has previous Premier League experience with Hull City.