The Reds have been linked with Asensio for a long time now and the latest reports are suggesting that they will finally make a concrete offer for the 26-year-old.
According to Spanish outlet AS, AC Milan are pushing to sign the Los Blancos playmaker, but they are unable to meet the player's steep demands.
The publication has claimed that the European champions are looking for a fee in the region of 40 million euros (£34.4 million) for the Spanish international.
However, the recently crowned Serie A champions cannot afford to pay that sum and at most, they will be able to offer up a mere 30 million euros.
As far as personal terms are concerned, the Rossoneri are looking to secure Asensio on a deal worth £75,000 a week, while Liverpool are able to offer a significantly more lucrative deal with the Spaniard.
The Madrid-based media outlet state that the Merseyside club have already made an offer for the player to earn £100,000 a week (6 million euros a year).
While the Italian giants aren’t expected to throw in the towel in this race just yet, it’s likely that Liverpool would be about to financially outmuscle them in any serious bidding war.
After making Benfica’s Darwin Nunez their marquee summer signing, Jurgen Klopp is ready to bolster his midfield options in this window after also adding two youngsters in Calvin Ramsay and Fabio Carvalho.
With Takumi Minamino leaving for Monaco, Divock Origi joining Milan and Sadio Mane having completed his switch to Bayern Munich, the Reds are significantly more depleted in attacking areas than they were.
With the likes of Naby Keita and Alex Oxlade-Chamberlain’s futures in doubt, they’ll also potentially be short in the middle of the park.
This explains the interest in Asensio who can operate both deeper in midfield and out wide as part of a front three.