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The 24yearold striker wrote on Twitter at the weekend: "Thanks everyone for the support. I really wanna thanks everybody. My family thanks all of you too."
Liverpool confirmed that Mario Balotelli had been given leave but insist that the details remain private.
The club depart for their pre-season tour to the Far East and Australia this weekend and the Italian international is expected to join up with the squad at some stage.
Liverpool have already reinforced their attacking options with the acquisition of England U21 striker Danny Ings from Burnley and Brazil international Roberto Firmino from TSG Hoffenheim.
Divock Origi has also joined his new team-mates after remaining on loan with Lille last season, while Liverpool have also been linked with a move for fellow Belgian international Christian Benteke from Aston Villa.