According to reports from El Mundo Deportivo, Kenny Dalglish has looked to make a swoop in the January transfer window for the Mali star, but will be facing tough opposition in the form of Russian big-spenders Anzhi Makhachkala, who are also keen on the player.
The 31-year-old is in the late stages of his career, and has only started five of Barcelona's 11 La Liga games this season, and could look for a big pay-day with a move to Russia to join Roberto Carlos and ex-team-mate Samuel Eto'o.
This would mark the end of his time with Pep Guardiola, as Keita was the Catalan's first signing from Sevilla in 2008.
His current deal with Barcelona runs till 2014, which would give the La Liga giants' bargaining power, and it is expected that Keita will cost at least £14 million, with a bidding war from the Merseyside and Russian clubs looking likely to push the price higher.
A versatile midfielder, he can operate as both a central or defensive midfielder, which would increase his attractiveness to both clubs.