The replacement for Paul Konchesky is thought to be Kenny Dalglish's main transfer priority at Anfield.
Taye Taiwo, Fabio Coentrao and Oscar Wendt are just three names to have been mentioned with Liverpool in recent weeks, although Enrique is thought to be the top target.
The national paper goes on to claim that Liverpool could look to push through a deal for Jose Enrique in order to avoid a transfer tussle with Serie 'A' giants AC Milan.