The Guardian reported on their website that Mancini spoke to the wealthy Ligue 2 outfit earlier this year with a view to joining them at the end of the last campaign.
It is claimed the Italian was offered a big-money contract and that the club expected him to sign. All this, it is reported, occurred before Mancini led City to the Barclays Premier League title and subsequently signed a new five-year contract at the Etihad Stadium over the summer.
The 47-year-old has enjoyed considerable success at City since succeeding Mark Hughes in December 2009.
He oversaw the end of the club's 35-year trophy drought by guiding them to their FA Cup win in 2011 and then masterminded that first league crown in 44 years last season.