Walcott is thought to be available, after struggling for starts at Arsenal this season.
West Ham are now in competition with Southampton, Everton and Newcastle United for the England international’s signature.
Moyes is thought to be keen to add quality to his squad this month, and Walcott has reportedly been identified as a target.
The Hammers want to take Walcott on loan for the season, with a view to making the move permanent at the end of the season.
Walcott would add pace to West Ham’s front line, and could be crucial for Moyes’ side as they look to avoid relegation.
The Hammers are currently sitting outside the bottom three, but they are far from safe.
Walcott has played just 49 minutes of Premier League football for Arsenal this term, which means that the 28-year-old could be keen to leave the Emirates Stadium, if the opportunity presents itself over the coming weeks.