Spanish newspaper Mundo Deportivo, as quoted by the Daily Mirror, is reporting that the Reds are preparing to make a fresh move to try and bring the 23-year-old to Anfield this summer.
Although Asensio has a contract at the Bernabeu until 2023 and a €700m release clause, the same report says that the Merseyside outfit are ready to try and sign him this summer.
Asensio has struggled to hold down a regular starting spot in the first team at Real Madrid this season and he has been limited to just 18 starts in La Liga.
He has scored one goal and made four assists in a total of 28 La Liga games for the Spanish giants so far this season.
With Liverpool FC having reached the Champions League final and still having hope of winning the Premier League this season, the Reds are not expected to make huge changes to their squad this summer.
But according to the same story, Jurgen Klopp is keen to bolster his attacking options ahead of next term, and Asensio could fit the bill.
Liverpool FC will take on Wolves in their final game of the season in the Premier League on Sunday.
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