The Southampton defender has been linked with a move to Jurgen Klopp's side, but according to 'Sky Sports', the Reds will not make a move for the Portugal international.
Liverpool are currently short of central defenders, with Dejan Lovren, Joel Matip and Ragnar Klavan the only recognised central defenders in the Reds squad.
Fonte is free to leave Southampton after the defender handed in a transfer request at St Mary's. The 33-year-old has 18 month to run on his contract, but claimed that he had not been offered a new deal with the club and has therefore asked to leave.
Manchester United have also been linked with the Saints player, along with West Ham, Everton and Crystal Palace.