The Hammers are looking to take advantage of the extended transfer window that allows Premier League and EFL clubs to do business.
And it is reported that they are close to an agreement with Brentford for Benrahma, 25.
The Algeria winger has been one of the best players in the Championship over the past year and has attracted plenty of interest.
However, none met Brentford’s asking price during the regular transfer window.
Benrahma was on the score-sheet twice against Premier League opposition last week in Brentford’s Carabao Cup win over Fulham.
Last season he scored 17 goals and contributed 10 assists in the Championship.
He could be showcasing his talents in the top flight soon if West Ham get a deal over the line.
Sky Sports also states that Crystal Palace retain an interest in the former Nice player.