According to the Athletic, West Ham are hoping to take advantage of that elongated domestic window by recruiting Benrahma, who has been linked with a host of Premier League sides after failing to earn promotion to the division last season following the play-off loss to Fulham.
The Hammers were one of the quieter teams in the summer transfer window, only securing a permanent deal for Tomas Soucek and a transfer for right-back Vladimir Coufal from Slavia Prague.
But they are interested in a securing a double signing before Friday, with Josh King of Bournemouth also on their list of targets.
They have already had a bid of £13m rejected by the Cherries, who are holding out for closer to £18m.
With regards to Benrahma, the Algerian is keep on a move away from Brentford to join a team in the Premier League, but the Championship side were less keen to let him leave after allowing another one of their star forwards from last season, Ollie Watkins, leave for Aston Villa.