Florentino Perez has been searching for a star man between the posts for a while now and has reportedly fixated his sights on the World Cup Golden Glove victor.
The Reds are now expected to hold talks with the Brazil worldwide.
While that strengthening further up the field will undoubtedly help Liverpool, goalkeeper is an obvious area for improvement.
A new goalkeeper has been needed at Liverpool for quite some time but recent events have given Klopp no choice.
Liverpool's bid worth £62 million falls slightly short of AS Roma's £66 million valuation, which seems to have given the Blues some late hope in their pursuit of Alisson. Chelsea have also been rumoured to enter the bidding, but Jurgen Klopp's men are closest to signing the 25-year-old.
Chelsea are in the running but have not made a second bid since Roma rejected their opening offer of around £44m.
Alisson representatives are understood to be thrashing out a long-term deal, believed to be for five-years, and he should be sealed and signed by Friday.
Another Brazil global in Liverpool's sights is midfielder Bernard, who is also wanted by Arsenal and Everton.