Manchester United, Chelsea and his former Inter boss Roberto Mancini at Manchester City have all been linked by media with the mercurial 19-year-old striker despite his misdemeanours.
Inter have said he is not on the market but club president Massimo Moratti implied he could still be sold.
"We don't completely reject an offer without hearing it and we don't put the phone down on anyone," he told reporters.
Balotelli, a confessed AC Milan fan, annoyed Inter by wearing their rival's strip on an Italian TV show earlier this year and even tough taskmaster Jose Mourinho failed to control him during Inter's treble success.
The Portuguese, now Real Madrid boss, gave Balotelli "a mark close to zero" for his display in a draw with AS Roma last year and dropped him from the squad for a month in March after a row.
YOUNG ITALIANS
Inter, whose starting lineup in May's Champions League final did not contain an Italian, would almost certainly not be mulling the sale of their top homegrown player before the season if Balotelli had not caused disharmony in the dressing room.
His antics cost the uncapped striker a place at the World Cup finals but, as the national team's dreadful showing proved, Serie A is crying out for young Italians to shine amid a dearth of domestic talent.
A move abroad, though, could be just what Balotelli needs to help him mature after just nine league goals last term.
"I agree that he is talented enough, a footballer who can change a match with his abilities," former Italy midfielder Stefano Fiore told Reuters.
Italian football's racism problem is another reason why a transfer to the more multicultural Premier League could benefit Balotelli, born in Italy but of Ghanaian descent.
He has been the subject of racist chanting, particularly from Juventus fans, and has sometimes reacted with angry gestures, comments or outrageous play-acting.
"I'm not sure it is racism in the strictest sense, because I think lots of idiots insult a player to target them and not because they consider them different because of the colour of their skin," Fiore added.
"It'll take time to defeat these idiots."
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
