Reports in Portugal claim Martins, 22, is the Reds' latest target as talks over Salah stalled after Liverpool's opening offer of £28m was rejected.
Roma are believed to want even more than the £40m touted as the original price tag for the 24-year-old Egypt international - leaving Liverpool to consider moving on alternative targets unless the Italian side compromise.
Liverpool are understood to have now made contact with Sporting for Portugal international Martins, who has a release clause of about £50m.
But this is likely to be negotiable as Sporting have not automatically qualified for the Champions League group stage and are facing financial pressures.