The Manchester City striker is understood to have opened up to friends about his difficulties in adapting to England.
Milan will continue to monitor Balotelli's happiness, despite the 20-year-old declaring he was happy to stay at Eastlands after scoring a hat-trick in Tuesday's 4-0 thrashing of Aston Villa.
Feeling Blue: Mario Balotelli is apparently unhappy in Manchester, but still managed to net a hat-trick against Aston Villa on Tuesday
The former Inter Milan player has never hidden his love of the Rossoneri and Allegri has fuelled the transfer talk by admitting: 'I would like to coach Balotelli, but it (a transfer) would be hard as we already have many champions.'
Milan chief executive Adriano Galliani is also a keen admirer of the Italy international and believes a deal at the end of the season is not impossible if Balotelli is still having problems.
To and fro: On-loan Milan striker Zlatan Ibrahimovic could return to Barcelona should Balotelli become available at a decent price
City boss Roberto Mancini has noted that his £23million summer signing never smiles, but Balotelli said this week: 'I am happy, even when I don't smile. I feel a striker has to score. It is my job. That is why I don't smile.
'I am very happy here, even if the journalists in Italy say I want to go to Milan. I am working hard in training and I want to be an important man for this team.'
Ronaldinho's expected January exit could mean a loan move for Luca Toni, but Milan are unlikely to commit to a permanent deal for the Genoa striker unless they are persuaded there is no chance of City selling their No 45.
Antonio Cassano was recently added to a list of forwards that includes Robinho, Zlatan Ibrahimovic and the returning Alexandre Pato.
But Ibrahimovic could return to Barcelona at the end of the season if there is better value to be had elsewhere in the transfer market.
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