The Spanish playmaker has been on the Reds’ radar for some time after starring for Los Che this term.
Scouts from the Merseyside giants have frequently travelled to the Mestalla to assess the silky passer, and have been impressed by his displays.
With Champions League football back at Anfield next season, Brendan Rodgers is keen to bulk up his squad with one or two top class signings, and Parejo is seen as a player capable of adding quality to their ranks by the Northern Irishman.
Valencia are desperate to keep the 25-year-old, but an offer of just over £20m will activate a clause in his deal allowing him to walk away should he agree a contract with Liverpool.
The former Real Madrid man is also wanted by Atletico Madrid, but he could be tempted by a return to English football – where he enjoyed a brief spell on loan at QPR as a youngster.
Parejo could be an alternative to top target Adam Lallana, with Southampton holding out for £25m for their captain.
However with £60m plus revenue from player sales at his disposal, Rodgers may look to draft in both players to support Jordan Henderson, Philippe Coutinho, Joe Allen and Steven Gerrard.