The duo arrived at Anfield for a combined figure in the region of £20m, and have just one Premier League goal between them – scored by the veteran Scouser.
This has led to claims that both will be sold, particularly amid rumours that the club are looking to re-call Divock Origi from his loan spell at Lille – which would cost them £5m.
However, Liverpool are prepared to give Lambert another chance, while interest in Balotelli is low.
The former has been linked with a loan move to Crystal Palace, but Rodgers is keen to ensure the 32-year-old stays.
Balotelli though will be allowed to leave should concrete interest emerge.
Greek side Olympiakos are the latest club to have been aligned with the player, yet there are suggestions they may be unable to make a swoop.
Fabio Borini is player the club are keen to sell, yet his £14m price-tag is pricing suitors out of the market.