The 25-year-old has recently returned to the Merseyside club after a disappointing loan spell with AC Milan.
Calabrian club Crotone will be playing in Italy's top division for the first time in their history next season and want a player such as Balotelli to join their ranks.
"I made a phone call to agent Mino Raiola for Balotelli," Crotone's president Raffaele Vrenna told La GazzaMercato.
"Crotone are the ideal environment for young talent to grow and express themselves.
"We could be the right place to revive an incredible talent like that of Balotelli, who has unfortunately just experienced a couple of difficult seasons."