Munoz, 22, is part of Spain's World Cup squad, and Liverpool have staff in the United States to conduct his medical.
Newcastle United had been in advanced talks to sign the winger, having sold Anthony Gordon to Barcelona, but Liverpool moved decisively to win the race for his signature.
The move will become Liverpool's first signing since Andoni Iraola replaced Arne Slot as head coach earlier this month.
Iraola's side are understood to be in the market for attacking reinforcements following the departure of Mohamed Salah, with Hugo Ekitike's recovery from a serious Achilles injury also expected to keep him out of action for an extended period.
Munoz scored six goals and provided two assists in 34 La Liga appearances for Osasuna last season, having joined the club from Real Madrid's academy system in 2025.
He also made senior appearances for Real Madrid before that move, and has previously come through both the Barcelona and Real Madrid youth set-ups.
The winger can operate across the front line, with his directness and ability to attack defenders in transition seen as a good fit for Iraola's preferred style of play.
Liverpool's decision to act swiftly mirrors their approach to Ekitike's own transfer a year earlier, when the Reds similarly moved ahead of Newcastle to complete a deal.
Munoz is yet to feature for Spain at the World Cup having not been used in their opening group fixture, but his rising profile both for his country and at club level has accelerated interest from England's leading clubs this summer.
Personal terms are understood to have been agreed in principle, with the move expected to be finalised once his medical is completed.
The transfer represents an early statement of intent from Iraola, who takes charge of a Liverpool side aiming to bounce back from a disappointing campaign in which they finished outside the Champions League qualification places.
Securing Munoz ahead of Newcastle will also be seen as a notable coup given how advanced talks between the Spaniard and the Magpies had reportedly become before Liverpool's intervention.
Liverpool's recruitment team are understood to have moved quickly once they identified Munoz as a viable alternative to other wide targets they have been tracking, with his versatility across multiple attacking positions seen as a particular asset.
The Reds are expected to remain active in the market throughout the rest of the window as Iraola looks to reshape his squad following his first summer in charge at Anfield.