Balotelli, 28, was reportedly informed not to return to the Ligue 1 club by Vieira this week after his tumultuous off-season resulted in a rather poor string of performances during the 2018/19 season.
The former AC Milan hitman was aiming to leave the French side but after a lack of suitors, he remained at the Allianz Riviera.
However, since returning to full fitness after missing out on pre-season preparation, Vieira is ready to part ways with the eccentric forward.
"I have given Mario a few extra days off to think about his future and what he wants to do," said Vieira, as per AFP.
"He's under contract here and everything is possible if we can come to a common agreement who knows."
Newcastle United have emerged as the leading favourites to land his signature, with manager Rafael Benitez keen to add some firepower into his faltering attack.
According to The Mirror, the Spaniard feels the gamble of the Italian could inspire them to safety in the English top-flight this season.
The Magpies are currently in 15th place, just two points away from the drop zone.