Michel, who is out of work following an ill-fated spell at Marseille, was previously in charge of Olympiakos, the club owned by Forest's prospective new owner Evangelos Marinakis.
The 53-year-old won two Super League titles and a domestic cup during his time at the Karaiskakis Stadium, which was ended prematurely by Marinakis in January 2015.
Last week it was reported that Forest, who sacked Dougie Freedman in March, have drawn up a fresh list of managerial targets after missing out on first choice option, Gus Poyet.
And Michel's odds have shortened from 14/1 to 8/1 in the space of 24 hours.
Joint top scorer in the 1987-88 European Cup, Michel spent 12 seasons a Real Madrid player and, having ended his career in Mexico, returned to his hometown to manage Rayo Vallecano and Getafe, either side of a spell in charge of the Blancos' Castilla team.
Post-Getafe, Michel endured a frustrating 13 months as Sevilla boss, but went on to record an impressive 71 per cent win ratio in Greece.