Graham left Australia's second-newest franchise after agreeing to join the Reds next season and the Force have been led by former assistant coaches Phil Blake, Nick Stiles and Andrew Scotney for the six games that have followed.
A number of high-profile candidates have been linked with the position, including a few who are well known for their achievements on this side of the equator.
Ex Leinster boss Michael Cheika, who led the Dublin-based outfit to their first Heineken Cup crown in 2009, is the bookies' favourite following his departure from French side Stade Francais.
But former Wales, USA and Ospreys supremo Scott Johnson is also thought to be in the mix, as is Steve Meehan who used to be with Bath, while Ireland coach Eddie O'Sullivan could be in line for a back-room role if he doesn't get the top job.
"We're trying to get this done as quickly as we can, but we also know we have to make the right decision," said Western Force chief executive Vern Reid.
"Most of those who we've interviewed already have coaching contracts, so it would be unfair to identify them in this process."
Star openside David Pocock is out of contract at the end of the season but the Force have kept him informed of the developments in their search for a coach as they look to do everything possible to prevent him from moving on.
"They (Pocock and Nathan Sharpe) are not involved in speaking with the candidates, but they're aware and they're supportive of who we've interviewed," added Reid, whose franchise face the Lions for the first time on June 5 next year.
"We've been in very earnest discussions with David (about his contract) for a long time.
"We're aware of his immediate aims and we're very astutely trying to accommodate his wishes. We're certainly doing everything we possibly can to keep him in Perth."