Manchester City believe Mario Balotelli could be bought by Milan, despite Silvio Berlusconi branding him a "rotten apple", and the Premier League champions are willing to accept about €30m (£24.6m) for the troubled striker.

That equates to the fee City paid in 2010 for Balotelli to Internazionale, who have first refusal on the player. There is a sense that the comments from Berlusconi, Milan's owner, about Balotelli potentially having a detrimental effect on the club's changing room may not represent the view of Massimiliano Allegri, the head coach, or other key members of the Rossoneri's management.

Roberto Mancini and City continue to back Balotelli in public but privately the striker's continuing erratic behaviour on the field and away from the game has exhausted patience. Last week's training-ground dispute between Mancini and Balotelli, in which the manager attempted forcibly to push the forward off the field for a bad tackle on Scott Sinclair, was the tipping point.

Although Mancini continues to admire Balotelli's talent and holds out hope that the 22-year-old could become one of Europe's premier strikers, were Milan – or any club – to make an offer near City's valuation, he could be sold.

Serious consideration is being given to bringing in a central defender this month. With Kolo Touré potentially absent until mid-February should Ivory Coast reach the Africa Cup of Nations final, City have only three experienced players in that position: Vincent Kompany, Matija Nastasic and Joleon Lescott.

Dedryck Boyata has been recalled from his loan spell at FC Twente but Mancini would like a defender of first-team calibre. The manager would prefer a permanent signing rather than a loan deal, with Everton's Sylvain Distin, a former City defender whose contract expires in the summer, broadly fitting the profile.

Sergio Agüero looks certain to miss City's trip to Arsenal on Sunday due to the torn hamstring he suffered during the 3-0 win over Stoke City on New Year's Day. The forward is back from Italy, where he received treatment on the muscle from a specialist, and although there is a remote chance he could be in the squad on Sunday – when City could start 10 points behind United, who kick off earlier against Liverpool at Old Trafford – the following week's visit of Fulham is a more realistic return date.

Mancini will not face any action from the Football Association over his comment following City's Boxing Day defeat at Sunderland that the referee Kevin Friend "ate too much". If found guilty of misconduct the manager might have faced a fine or a touchline ban.

The Italian wrote to the FA to explain his words last week, with the governing body responding on Monday to remind Mancini of his responsibilities. The matter is now closed.

City lost 1-0 to Sunderland, with Mancini believing his team should have been awarded a free-kick during the build-up to Adam Johnson's winner.

The manager said later: "The referee may have had too much to eat for Christmas. He and the linesman too. It wasn't a great game from them. That's the problem we have sometimes in football. I don't see how the referee can't see the foul in the buildup. I don't know how."