The 25-year-old winger is yet to finalize personal terms with the Irons.
Benrahma contributed 17 goals and nine assists as the Bees narrowly missed out on promotion to the Premier League last season. West Ham have tracked the artful Algerian for much of the summer with David Moyes seeking more inventiveness in his squad.
The Irons' apparent dearth of creativity became more clear after Felipe Anderson's completed loan switch to FC Porto on deadline day.
West Ham have also had Bournemouth reject a £13-million bid for Joshua King, according to The Guardian's Jacob Steinberg, but the club expects to sign center-back Craig Dawson from Watford for no more than £4 million.
English football's domestic transfer window closes next Friday.