Former Inter, Manchester City, Liverpool and Milan forward Balotelli spent last season in Turkey with Adana Demirspor.
The Italy international scored 18 Turkish Super Lig goals as the team finished ninth, with only Kasimpasa's Umut Bozok managing more strikes in the competition (20).
That tally included a stunning five-goal haul on the final day against Goztepe, making top-flight history for Adana Demirspor in the process.
Balotelli is under contract until 2024, though the 31-year-old seems to be pushing for a move away, having suggested he could move to LaLiga, with Valencia said to be interested.
However, Sion's president Christian Constantin has confirmed his team are in discussions with the player.
In an interview with the Swiss-German publication Blick, Constantin said: "It's true. We've been in talks for weeks.
"Today it is impossible for me to make a forecast about the chances of success of the transfer.
"We wanted to remain discreet, but the information apparently leaked in Italy. This is a signal that there is interest on both sides."
Signing Balotelli would represent a coup for Sion, who will be looking to improve on a seventh-place finish last season, with their Swiss Super League campaign starting on Sunday.
"If you only talk about talent, Mario had what it takes to win the Ballon d'Or," Constantin added.
Constantin also revealed Sion were interested in signing Balotelli back in 2016, before the forward moved to Nice.
"The first time we spoke to [Balotelli's former agent] Mino [Raiola] about Mario was in 2016, before he signed in Nice," Constantin added.
The president's son Barthelemy, Sion's sporting director, added: "We've been in contact with his agents for a long time and have a good relationship. We've done a few deals together in the past."
The 32-year-old Cameroonian was one of nine players to lose his job when the Swiss side offered a reduced wage package as an emergency coronavirus measure.
According to Sion, Song and eight team-mates refused the new terms and were dismissed with immediate effect.
With income severely hit, given the Swiss Super League is suspended, Sion president Christian Constantin is confident the club were acting responsibly in proposing the new wage measures.
Yet Song, 32, is far from happy with the situation and intends to take legal action, with the Swiss players' union also indicating its support for the footballers in the past week.
"My lawyer will take care of it, it's gone to FIFA. We're going to defend our right," Song told French broadcaster RMC.
He explained: "We played a friendly on Friday and we were supposed to meet with the president on Monday, then Tuesday. We had no news. We received a WhatsApp message on Tuesday afternoon to tell us that everyone had to sign a paper saying that we'd reduce our salaries, that we'd be paid around 12,000 euros.
"We had to return the paper by 12pm the next day. We received this document without an explanation."
Song said that without speaking to the club, it would not have been right to sign up to the new arrangement.
"We decided together to not sign this document," he said. "We wanted to discuss it."
Sion, for their part, said players were invited by the club's accounting department to participate in a video call, but that few took up the opportunity.
Former Camp Nou and Emirates Stadium star Song remains bewildered by Sion's swift move to cull players who did not immediately fall into line.
"I've not committed any professional mistake," he said. "Every club talks to their players to reach solutions. I don't understand what's happened. Nobody can understand it."
Grosso started his senior managerial career with Bari in 2017 before joining Hellas Verona in 2018.
Following his dismissal in May 2019, he took over Serie A club Brescia in November but was sacked after just three games in charge.
Sion finished eighth in the 10-team Swiss Super League last season, avoiding a relegation play-off by just one point.
