The young Denmark international has 12 months left on his contract with the Dutch giants and is unlikely to extend his stay at the Amsterdam Arena.
Liverpool will face stiff competition from Tottenham but the Reds have been scouting the 21-year old for over a year. Liverpool wouldn't want the same situation in the transfer market like last summer and are prepared to bring in players to strengthen the squad.
Liverpool centre half Daniel Agger is Eriksen's captain at international level and the player has played alongside Luis Suarez at Ajax.
Brendan Rodgers has earlier mentioned that he needs three or four players in every position to improve his squad. Liverpool have been linked with Newcastle's Hatem Ben Arfa, Henrikh Mkhitaryan of Shakhtar Donetsk and Swansea's Ashley Williams.
Rodgers wants a reunion with Willams to fill the gap left by Jamie Carragher, who is set to retire at the end of the season, and Martin Skrtel's future at Anfield is uncertain.
Skrtel's agent Karol Ksonto has denied any links with other clubs but the central defender has been targetted by Russian cash-rich club Anzhi Makhachkala.
Liverpool are also chasing Blackpool winger Tom Ince, while Rodgers is interested in Paris St. Germain forward Kevin Gameiro.