Jurgen Klopp has enjoyed a productive summer transfer window so far, adding as many as three players to his first-team squad at Anfield.
There has been talk that Klopp may not make any further changes to a squad which challenged on four fronts last year, lifting two pieces of silverware and finishing as runners-up in the Premier League and Champions League.
The 26-year-old has spent much of his senior days at the Santiago Bernabeu, contributing 49 goals from 235 appearances in all competitions.
Asensio has fallen down the pecking order under Carlo Ancelotti, however, with 12 of his 31 La Liga outings during the most recent campaign coming from the substitutes' bench.
With just one year remaining on the playmaker's contract, there is seemingly a reluctance in both camps to sign extended terms at Los Blancos.
While there is a willingness from Asensio to move to a new club, it is been widely claimed that he only wants to join a team where he will be first choice.
The same report claims that Asensio has also received an offer from AC Milan, who were first linked with him ahead of the January window.
Real Madrid are said to be looking for a fee in the region of £35m, while Asensio allegedly wants to earn in the region of €7m (£6m) per year at his next club.
However, both parties may have to be open to a compromise in order to facilitate a transfer before the end of August. body check tags ::