The Spanish playmaker has been earning rave reviews for his performances in La Liga this term, where he has now established himself as a first-team regular at the Mestalla.
It is understood that Brendan Rodgers has been tracking the silky passer for some time, and has had chief scout Barry Hunter monitoring his progress over the course of the past month.
The Northern Irishman is known to be in the market for reinforcements when the summer transfer window opens, and a central midfielder is said to be a priority.
Although he already has Lucas, Jordan Henderson, Joe Allen, Philippe Coutinho and talismanic skipper Steven Gerrard at his disposal, the Anfield boss is desperate to add further to his ranks as he prepares for what looks likely to be a 2014/15 campaign including Champions League football.
Parejo, 24, is seen as the ideal man to add yet more creative spark to the Reds’ armoury, and fits the club’s policy of buying younger players.
The former Real Madrid trainee has already spent a brief spell in English football with QPR in 2008, but he failed to make an impact at Loftus Road as an emerging talent.
Valencia are keen to keep their man, but Parejo may be open to a switch to Liverpool.