Yossi Benayoun's imminent move to Chelsea could spark an exodus from Liverpool.
The Israel midfielder is expected to join Chelsea this week.
And The Times says a number of other players are up for sale, with Liverpool open to offers for Ryan Babel, Albert Riera and Philipp Degen, among others.
Diego Cavalieri, the club's second-choice goalkeeper, is seeking a transfer to secure regular first-team football, having been understudy to Pepe Reina for two years.