Atletico sporting director Jesus Garcia Pitarch has talked to Liverpool boss Rafa Benitez about signing the 28-year-old.
The Italian full-back has failed to make an impact at Anfield since joining the club from Udinese for £7million 18 months ago.
Dossena is reportedly prefering a return to Italy and Roma have shown interest in the defender.
The Mirror says Atletico Madrid are ready to pay £2million for the defender.
