A prominent member of France's 1998 World Cup-winning squad, Blanc guided Girondins Bordeaux to the Ligue 1 title last year, in only his second season as a coach and a repeat of that triumph was considered a formality at the start of this year.
The last few weeks, however, have been tough on Blanc and his side, who have slipped down to sixth place, 11 points behind leaders Olympique Marseille, with six matches remaining.
Bordeaux have all but given up on defending their title after picking up one point from their last four matches and to rub salt into their wounds, they were also knocked out of the Champions League by Ligue 1 rivals Olympique Lyon in the quarter-finals.
The poor run has put a strain on Blanc, who lost his trademark cool exterior in the process, blaming his players instead of accepting responsibility.
The 44-year-old remains, however, the most likely candidate to replace the controversial Domenech, whose contract ends after the World Cup, to the extent that French media reported last week he had already made his decision.
Blanc dismissed the report as "absolute nonsense" and reminded the media he had other things to worry about.
"I am not saying anything about it (the France job) because I don't want to talk about it," Blanc told reporters. "What I want is for us (Bordeaux) to finish the season the best we can."
This was the second time in a matter of months that Blanc denied a report saying he had agreed to leave Bordeaux and succeed Domenech after the World Cup.
More reports and more denials should follow until the French Football Federation (FFF) makes an official announcement, expected during a council meeting in Paris on May 20.
FFF president Jean-Pierre Escalettes, who has faced criticism for ruling that the unpopular Domenech should stay on until the World Cup, has described Blanc as an "exemplary man" and a "good candidate" for the France job.
Escalettes made sure, however, that an air of mystery over Domenech's successor would remain by naming World Cup winner Didier Deschamps, former France midfielder Jean Tigana and current assistant coach Alain Boghossian as other possible replacements.
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