The Liverpool Echo says the Reds have other targets as a priority this summer.
Reports in France this week suggested that Liverpool's hopes of signing him had been bolstered by his refusal to pen a new contract.
However, the Reds are no longer pursuing the 22-year-old and are focusing their attention elsewhere.
His contribution this term has been considerably less impressive with three goals and five assists.
The club's recruitment team, which includes Dave Fallows and Barry Hunter as well as manager Jurgen Klopp and sports chief Michael Edwards, are convinced that there are other players in that position who will be available this summer and are more suited to what Liverpool require.