The Liverpool legend now TV pundit suggested that Rodgers' experience of managing Luis Suarez - who left the club this summer for £75 million - could be useful experience if the Italian completes his move to Merseyside.
Carragher told Sky Sports: “The main thing for any player is what they do on the pitch. Both of those players had issues off the pitch, but I think it’s fair to say Suarez did a lot more on the pitch.
“You will always get a little bit more freedom if you’re producing on the pitch, that’s the main thing for any player.
“Balotelli is a player who has been here before and did a lot of stuff that was good for us in the media. He probably didn’t quite show his potential at Manchester City and that, coupled with his off-the-field problems, probably saw him depart."
The need for Liverpool to sign a new striker has been pretty clear this summer since the departure of Suarez. The Reds tried to secure the services of Loic Remy from Queens Park Rangers only to pull out at the last minute because of concerns that showed up during the Frenchman's medical.
Only Daniel Sturridge and Rickie Lambert were available for Liverpool's opening day victory against Southampton - whilst the future of Fabio Borini remains uncertain after a £14 million bid was accepted from Sunderland for his services, though it looks unlikely he will move to the North East.
Inevitably there will be a lot of talk surrounding the Italian's reputation for his antics off the field as well as on it, but the Reds now look as if they are signing a striker of proven quality who has experience of winning titles.