Leach reached a verbal agreement to replace Paul Wulff, but has not signed a contract, according to an official in the athletic department who spoke on condition of anonymity because he was not authorized to comment publicly on the matter.
Leach posted an 84-43 record at Texas Tech, leading the Red Raiders to 10 bowl appearances in 10 seasons. He was fired in 2009 amid allegations he mistreated a player with a concussion.
CBSSports.com first reported that Leach had reached an agreement with Washington State.
Wulff was fired Tuesday after four losing seasons.
Leach was at the top of athletic director Bill Moos' list of candidates, in part because Moos wants a high-powered offense at WSU. While at Texas Tech, Leach's Air Raid offense routinely led the nation in passing and set numerous records.
Leach was offensive coordinator at Kentucky and Oklahoma before becoming the Red Raiders head coach in 2000.
In 2009, Texas Tech fired Leach two days after suspending him after it was alleged he mistreated receiver Adam James, who had a concussion. Leach denied the allegations and later sued for wrongful termination.
Leach has said he suspects an $800,000 bonus he was due the next day was the reason he was fired.
In a separate case, Leach has also sued ESPN Inc. and a Dallas public relations firm, accusing them of libel and slander after he was fired. James is the son of ESPN analyst Craig James.
Leach has been out of coaching the last two seasons. During that time he has put out two books, worked in television and hosted a satellite radio show.
Wulff was fired after posting a 9-40 record in four years during which he was charged with rebuilding a downtrodden football program. The Cougars finished 4-8 this season, the best record of his tenure.
Moos said Washington State needs to re-energize its fan base, in part to help pay for extensive renovations to Martin Stadium.
Construction has started on an $80 million project to add premium seating, luxury boxes and a new press box. Also on the drawing board is a $60 million football operations building.
Moos said at a news conference Tuesday afternoon that WSU was at a "critical" juncture during which the program needed to either move forward or be content with being a league doormat.