Rafa Benitez's side are already six points behind Chelsea following their third defeat of the season at Stamford Bridge on Sunday.
Now Italians Juve are planning a fresh bid for Argentine midfielder Mascherano, 24, who they tried to sign from West Ham before he moved to Anfield in January 2007.
The Turin giants are ready to offer £23million as they seek to grab the Serie A title away from Inter Milan.
And club officials plan to open talks with their Anfield opposite numbers in the coming weeks.
Mascherano is already a target for Barcelona, with Liverpool rejecting an ]approach for him from the European champions during the summer.
Mascherano, who possesses an Italian passport, is tempted to move away from Merseyside even though he is under contract until 2012.
He is believed to be unhappy at the break-up of his partnership with Xabi Alonso, who joined Real Madrid in the summer.
And he was dismayed at criticism for his performance in the 2-0 defeat at Chelsea.
The Kop have got their own back on Chelsea by stealing Benfica wonderkid Toni Brito Sa from under their noses.
Benfica have accepted Liverpool's offer of £290,000 for one of the most highly-rated youngsters in Portugal.
Guinea-born Brito, 16, had a trial at Chelsea when Phil Scolari was boss and was ready to sign a six-year deal.