The deal for the signing of the centre-forward is believed to be close to £30 million according to Sky Sports.
The 25-year-old delivered spectacular performances for the Bees in the 2019-20 season, scoring 17 goals in 43 league games to help the club reach the playoff final, where they lost against Fulham.
The forward, however, failed to make his dream move to the English top-flight before the end of the main transfer window.
The attacker will now hope to reach personal terms with the Hammers before the end of the domestic window between Premier League and EFL clubs on Friday.
The forward has since bagged more than 27 goals across all competitions for the Bees since his arrival at the club.
He will also be expected to play a part when the African champions take on Mexico in their second friendly on Tuesday.
Benrahma will hope to sort out his future on his return to England after the international break.
Should his move to West Ham be successful, the forward would link up with the Democratic Republic of the Congo international Arthur Masuaku at the club.
The Hammers narrowly escaped relegation last season after finishing 16th in the Premier League.
In the current campaign, David Moyes' men have won two games and lost two in four matches to be placed 10th on the standings.