"I have spoken to him about this," the manager told reporters. "He's not at the stage of his career where he should be battling with four or five other players for one or two positions... so it's clear we need a solution.
"There will be a club around who would be happy to have the new Mario Balotelli. I have spoken clearly to the player about that."
Sampdoria have expressed their interest in the player, with president Massimo Ferrero saying they would be the perfect club for him to revive his career after scoring just three goals in 23 appearances for Milan last season.
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Another player who is unlikely to be lining up for Liverpool for their Premier League opener against Arsenal on Aug. 14 is defender Mamadou Sakho, who underwent treatment for a long-standing Achilles problem.
The France international has not played since April after being informed by European football's governing body that he had failed a dope test.
UEFA dismissed the case against the 26-year-old last week, but Sakho missed Liverpool's Europa League final defeat by Sevilla in May and was dropped from France's squad for the European Championship as a result of the charge.
"Mama is injured. He had a little issue with his Achilles when he was playing, one day on, one off, this kind of thing," Klopp said.
"When he had his little 'break' he used the time to have a little bit of treatment and that now means another three or four weeks before he can train again."
Klopp did not want to get drawn into whether the matter was now closed.
"I cannot say too much as a manager," Klopp added. "I don't know exactly what will happen now from Mama's side or UEFA's side.
"Others have to talk about this because I don't know what I am allowed or able to say."
(Reporting by Simon Jennings in Bengaluru; Editing by Peter Rutherford)
