The newly promoted Premier League club want to ensure they have a squad that will not go straight back down.
And Benrahma, who got Brentford to within a playoff final of the league, is a key target.
The Mirror says Leeds are willing to break their transfer record for the £25 million-rated winger.
The Algerian has an £18 million buy out clause that may be active, as the club is no longer able to gain promotion for next season.
But it is unclear as to the legal parameters surrounding the buyout clause, and Leeds may still have to convince Brentford to accept a high bid for the player.