A picture agency has released photographs it says were taken on Thursday morning of the pair having to be separated by staff and team-mates at Carrington training ground.
City have declined to comment.
Mancini is expected to answer questions about the incident at his news conference on Friday morning.
"It's believed Mancini reacted to a challenge from Balotelli on one of his team-mates," said BBC radio 5 live senior football reporter Ian Dennis."In one of the photos Mancini is seen to be pulling at Balotelli's orange bib, and in another photo Balotelli is being restrained.
"I'm led to believe the incident blew over very quickly and with that in mind the photos do need to be put into some sort of context because super-fast frames can show the spat but don't necessarily provide a true reflection of any time period.
"However, it doesn't reflect well on the champions, it ensures Balotelli will create headlines yet again, and Mancini will be quizzed about his relationship with the player at tomorrow's press conference."
The pictures appear to show Mancini shouting and gesticulating towards Balotelli, who has scored three goals in 21 appearances this season.
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One photograph shows the pair face to face with Mancini pulling Balotelli's training bib, while in another, the striker appears to be pulled away by a member of staff.
The 22-year-old Italian has been involved in a series of controversies since his £24m move from Inter Milan in August 2010.
In December, Balotelli was set to take City to a tribunal over a two-week fine for missing 12 games last season because of suspensions.
He later dropped the action and accepted the punishment, prompting Mancini to say he was willing to give the striker another chance.
In November, Mancini said he had no intention of selling the player despite his tempestuous relationship with his fellow Italian. Last season, Balotelli scored 17 goals in all competitions for City but was sent off twice.
After his red card against Arsenal in April, Mancini cast doubt over Balotelli's future at the club saying he didn't "have any words for his behaviour".
Mancini has often talked about the challenges of managing the player he says could be one of the best in the world .
In April, the City manager joked he might have punched Balotelli in the head every day if he were his team-mate.
He said: "I don't speak with him every day, otherwise I would need a psychologist, but I speak with him because I don't want him to lose his quality."
But Mancini has also stated that Balotelli's behaviour on and off the pitch is blown out of proportion , saying "every time Mario does something, [it] is like a war".
This is not the first time the City manager has fallen out with one of his players.
He saw Carlos Tevez return home to Argentina following a row during the 2-1 defeat at Bayern Munich in September 2011.
Mancini claimed the striker failed to warm up and insisted Tevez would never play for the club again, while the forward complained of being treated "like a dog".
But the relationship was repaired and the forward returned to action in February 2012 and helped City win the Premier League title.
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