With Liverpool having failed to secure Lyon's Nabil Fekir the hunt is seemingly on for the Anfield outfit to find a suitable replacement to bolster their attack this summer, and the Spain international is reportedly the next name on the list.
Although the Reds have pushed out their transfer expenditure in recent years, with Virgil van Dijk currently holding the crown as their most expensive recruit (£75m), Mundo Deportivo have claimed the Merseysiders are prepared to blitz that fee out of the water.
The Spanish report claims a firm offer of €180m has been tabled by Liverpool to secure the services of the 22-year-old who has a €700m release clause in his current contract which runs until the summer of 2023.
The wide playmaker struggled to cement himself in Zinedine Zidane's startling lineup last season and whilst Lopetegui is fond of the young star having selected him as a member of Spain's World Cup squad, he could consider pursuing regular football elsewhere next.
Real president Florentino Perez is said to be plotting an overhaul of the squad and Asensio could find himself squeezed out of the Bernabeu, much to the delight of Jurgen Klopp who is said to be a long term admirer of Asensio.
Although Asensio has shown signs of becoming a world class talent, serious doubts remain over the Reds' willingness to spend a significant chunk of money on the player who made 48 appearances for Los Blancos last term, scoring nine goals and providing seven assists.