The 28-year-old made the switch to San Siro in August 2011 and was a mainstay in the side that reached the Champions League last season after a late resurgence.
However, the Italy international has struggled to maintain a regular spot in the Rossoneri XI this term, starting on just seven occasions in Serie A.
That has led to a temporary move to Sam Allardyce's side, which is desperate to bring in reinforcements as the club seeks to escape the Premier League relegation zone.
The Upton Park outfit currently sits 18th in England's top flight, having picked up just four wins from 22 matches thus far.
Nocerino could be joined at the London club by another Italy international in the form of Marco Borriello.
The forward has been strongly touted with a move to West Ham and said his goodbyes to Roma supporters on Twitter on Friday.
West Ham also had a bid rejected for Leeds United forward Ross McCormack on Friday.
Nocerino started his career at Juventus, where he enjoyed loan spells at Genoa, Messina and Piacenza, before making a permanent move to Palermo in 2008.