The Reds will listen to offers for the pair, who have both failed to force their way into the starting XI...
Netherlands international winger Babel recently suggested that he may look elsewhere for regular first-team football after admitting to becoming frustrated at frequently being names on the bench.
Italy international full-back Dossena, meanwhile, has also struggled to convince manager Rafael Benitez to name him in the starting XI on a regular basis since arriving from Udinese last summer.
Apparently, with Benitez hoping to sign a new full-back, a winger and a striker, any offers for the aforementioned duo will be seriously considered as funds are needed for incoming transfers.
Danish centre-back Daniel Agger might also leave the Merseyside-based outfit, even though Benitez appears to be keen to hold on to him. He is uncertain about signing a contract extension after losing his place in defence to Martin Skrtel.
The likes of Barcelona, Real Madrid and Milan are all thought to be keeping tabs on the 24-year-old defender.
With regards to who might be on Liverpool's wish-list, Aston Villa's Gareth Barry has cropped up once more, as has Valencia's David Silva.
However, while the Reds are likely to move for the former, it appears that they have ruled themselves out of the running for the latter.
"Our chief scout, Eduardo [Macia], was in Valencia and was talking with different people from the club, but someone was talking too much," Benitez is quoted as saying.
"So, at this moment, Silva is not a target. He is a good player, but not our target."
Ricky Brooks, Goal.com