How about Jesse Marsch?
Leeds play an exciting and progressive style of football entirely based around getting possession into key spaces and constantly trying for opportunities. This was pioneered by Marcelo Bielsa, but continued by RB Salzburg and RB Leipzig coach Marsch.
The American is a stylistic juggernaut. Gegenpressing football, aggressive football, progressive passing, etc. His Leeds were a creative force even without their major talents. They created the chances, exploited space, and played their entertaining brand of football. However, there is a caveat.
Defensively the English club were just as bad as Rodgers’ Leicester City. Once a turnover occurred, with any injuries to key players they would crumble and surrender a chance. The only thing they had was pace to trackback, their organisation was lacking. Marsch is not a defensive coach.
Additionally, price wise he should be decent. Certainly the American coach should cost less than the Northern Irish head coach. That being said, the manager would be more expensive than Benitez and likely would want to stay at the club. He might not accept a temporary position.