“I’d coach him, I spoke to him two years ago about bringing him to Sassuolo, but nothing came of it. He’s a player with huge potential,” said Di Francesco ahead of Saturday’s game against Serie A leaders Napoli.
The former Manchester City striker has hit top form for Nice this season with 21 goals.
Balotelli won six trophies with Inter Milan including the Champions League before moving to Manchester City in 2010, followed by two spells at AC Milan either side of an unsuccessful stint at Liverpool.
The 27-year-old left Liverpool on a free transfer in August 2016 to join Nice, who are ninth in the French league this season.
Balotelli’s agent Mino Raiola said on Thursday that he had spoken to Roma about signing his client.
“I’ve spoken with Juventus, Roma, Napoli and Inter,” said Raiola. “Mario is ready to return, he has matured into one of the top 10 strikers in the world.
“In Italy he’s number one. He’s worth 100 million euros, but he’s on a free transfer and is therefore a bargain.
“I’m already negotiating with many clubs in England and in Italy. I’ve spoken with Juve, Roma, Napoli and Inter.”
Roma have slipped out of the Champions League places to fifth ahead of Saturday’s game in Naples.
“We need to pick up results because the more we keep going like this, the less chance we have of getting back in the Champions League places,” said Di Francesco.