Asensio has been associated with the Reds for a while, and the most recent rumours indicate that they will eventually make a firm bid for the 26-year-old.
The Los Blancos playmaker is wanted by AC Milan, but they are unable to match his high demands, according to Spanish publication AS.
According to the magazine, the European champions are requesting a transfer price of around 40 million euros (£34.4 million) for the Spanish international.
The freshly crowned Serie A winners, however, are unable to pay that amount and will only be able to contribute 30 million euros at most.
The Rossoneri are seeking to recruit Asensio to a contract for £75,000 per week, but Liverpool can provide the Spaniard with a deal that is substantially more lucrative.
The Merseyside club has reportedly already made an offer for the star to earn £100,000 per week, according to the Madrid-based media site (6 million euros a year).
Although the Italian superpowers aren’t anticipated to give up on this pursuit just yet, it’s probable that Liverpool would soon outbid them financially in any significant bidding battle.
Jurgen Klopp is prepared to expand his midfield options in this transfer window after also bringing in two young players in Calvin Ramsay and Fabio Carvalho. Darwin Nunez of Benfica was their star summer acquisition.
The Reds are substantially less strong in offensive areas than they were before Takumi Minamino left for Monaco, Divock Origi joined Milan, and Sadio Mane finished his move to Bayern Munich.
They may also be short in the center of the park since players like Naby Keita and Alex Oxlade-futures Chamberlain’s are uncertain.
This explains why Asensio, who can play both wide and deeper in midfield as a member of a forward three, has drawn attention.