The sacked Reds boss has backed the Merseyside team to develop under his successor.
The Northern Irishman was relieved of his duties on Sunday following the 1-1 draw against Everton at Goodison Park in the Merseyside derby.
The former Swansea City boss had been under increasing pressure in recent weeks due to inconsistent performances on the pitch, with a significant section of the Kop starting to get restless due to poor displays.
Jurgen Klopp is currently the favourite to take over from Rodgers in the Reds hotseat, while Carlo Ancelotti is also being mentioned as a potential option.
In a parting statement, the sacked manager has stated that he expects Liverpool to excel under whoever takes over his position and praised the quality at the new man’s disposal.
“The current squad is one in transition, but they have some real talent and are showing a strong sense of togetherness,” The Guardian quote Rodgers as saying.
“I expect to see them continue to grow and develop over the coming weeks and I wish them and my successor well for the rest of the season.”
Liverpool sit in tenth place after eight games of the new Premier League season with 12 points; only six adrift of division leaders Manchester City and three behind the Champions League qualification places.
The Reds have high hopes of finishing in the top four this season after missing out last term.