The Spanish playmaker only joined Los Blancos last summer in a big money deal from Malaga, but is already thought to be looking to leave.
After making a blistering start to his career at the Bernabeu, the 21-year-old has struggled for playing time thanks to the presence of Gareth Bale and Luka Modric.
Brendan Rodgers is thought to be a fan of Isco, and is ready to make him his marquee arrival.
The youngster is unlikely to come cheap, and cost in the region of £30m.
Isco is being hailed as a potential long-term replacement for Steven Gerrard, with the 33-year-old entering the closing stages of his career.
The Red skipper has moved to a deeper role of late, which has left the club short of his influence in the final third.
The Merseysiders’ ability to lure Isco to Anfield may depend on their ability to qualify for the Champions League.
Manchester City and Arsenal are also looking at the silky passer, and could mount moves in six months’ time.