Dossena, a £7m buy from Udinese last summer, has told manager Rafael Benitez that he wants to leave Merseyside after failing to establish himself in the first-team last season.
The seven-times capped Italy left-back started just 12 Premier League games last season, with the Brazilian Fabio Aurelio restricting his opportunities.
And although Juventus are keen to take Dossena back to Italy, Liverpool are unlikely to recoup the money they spent on the 27-year-old just 12 months ago.
Dossena said: 'Before coming back to Italy I talked to Rafael Benitez and explained to him doubts.
'I told him I wanted to leave. He is an exceptional person and understood my problem.
'He told me that if they receive an offer that satisfies both the club and me, he will take it into consideration and try to facilitate my transfer.' Dossena, whose solitary league goal for Liverpool came in the 4-1 victory against Manchester United at Old Trafford in March, has admitted that he would welcome a move to Juventus.
He said: 'I would run to Juve. They showed interest in me last year, but then Liverpool stepped in and wrapped things up in less than an hour.
'Of course I would acc ept an offer. You're talking about one of the biggest clubs in Europe.'
Dossena's departure would leave Liverpool requiring cover for Aurelio at full-back, but it would also mark another costly transfer market mistake by Benitez.
The Liverpool manager sold Robbie Keane back to Spurs in £12m deal in January just six months after sanctioning a £20m move for the player.
Any fee for Dossena would help boost Benitez's summer transfer fund, however, in the light of the £42.6m losses run up by the holding company of Liverpool's owners, Tom Hicks and George Gillett.