The Reds are believed to have attempted a swoop for the 34-year-old in January, but their efforts ended in disappointment as he opted to pen a six-month deal at the Mestalla.
Although he is rumoured to be keen to stay, the Spanish side may opt against keeping the Malian veteran, with financial worries still gripping the La Liga giants.
Liverpool can offer a greater wage to the African enforcer, which may tempt him across to Merseyside.
Keita made over 100 appearances for Barcelona, where he won the Champions League in 2009 and 2011 as well as numerous other honours, before leaving to join Chinese side Dalian Aerbin in 2012.
His spell in the Far East was a short one, and he returned to Europe with Valencia just a few months ago after being released from his contract.
Anfield chief Brendan Rodgers is planning for a campaign of European and domestic action, and sees the experienced star as a player that will be able to contribute to his side’s efforts next term.
The Northern Irishman is also targeting Adam Lallana, Dejan Lovren and Rickie Lambert, and may use Keita as cover for Steven Gerrard.