Arsenal legend Vieira was axed by Nice in December after a poor run of form and the club’s Europa League departure, and the 44-year-old is now thought to be one of four candidates to take over from Garcia when he departs at the end of this season.
Lyon’s board are said to be increasingly receptive to the idea of appointing Vieira because he would be immediately available for no pay-off, according to L’Equipe.
Patrick Vieira (right) is said to be in the frame to succeed boss Rudi Garcia when he leaves Lyon
Vieira is looking for his first managerial role since leaving fellow Ligue 1 side Nice in December
Les Gones are also keen on Christophe Galtier, who is closing in on the Ligue 1 crown with Lille in a tight title race ahead of PSG and Lyon, and Sassuolo manager Roberto De Zerbi.
Ukrainian heavyweights Shakhtar Donetsk have also been strongly linked with De Zerbi, while Marcelo Gallardo, the other name in the reckoning, is understood to want to stay in Argentina with River Plate until the end of the calendar year.
The difficulties of pursuing managers already under contract could push Vieira to the top of the list, potentially handing him his first taste of Champions League football since he played for Inter Milan during their treble-winning 2009/10 campaign.
Lyon could also appoint Sporting Director Juninho, although that could land them penalties from the league as the former Brazil international does not currently hold the required qualifications to lead a team in the French top flight.
The 1998 World Cup and three-time Premier League winner is yet to win a trophy as a manager
Vieira has never won a trophy as a manager, winning 35 and losing 32 of his 89 games in charge of Nice from June 2018.
The three-time Premier League winner left his first job in France after a dismal European campaign in which Nice lost five games out of six in the group stage, including home defeats to Slavia Prague and Bayer Leverkusen.
Nice lured him from New York City, where he had guided the Major League Soccer side to their first ever playoff appearance during a reign that began at the start of 2016.
Manchester City gave him a development role following his retirement in 2011, and Newcastle interviewed Vieira for their managerial vacancy in May 2015.