The 29-year-old midfielder moved on loan from the Ligue 1 club to West Brom last September, and scored four goals in 30 outings.
Amalfitano started his career in France with Sedan before moving to Lorient for three season in 2008.
West Ham, have been linked with a number of players in the past week as manager Sam Allardyce looks to strengthen his squad further before the start of the season.
The Hammers have already signed Enner Valencia, Cheikhou Kouyate, Mauro Zarate, Aaron Cresswell and Diego Poyet on permanent deals, while Carl Jenkinson has joined on loan from Arsenal.
Not a bad signing, he was one of the better players at West Brom last season- shea666