Antonio Conte is believed to be on borrowed time at Stamford Bridge, with multiple media reports suggesting that the club board is looking for a replacement in the dugout.
Chelsea's interest was reportedly piqued by Zinedine Zidane's exit from Real Madrid, but the Frenchman is said to be finalising a deal to manage the Qatar national team through to the 2022 World Cup.
The Blues are also thought to have cooled their interest in former Napoli boss Maurizio Sarri and have instead sought to recruit Zidane's former France teammate Blanc.
The 52-year-old, who won a total of four Ligue 1 crowns with Bordeaux and Paris Saint-Germain, is a free agent and thus available to come immediately with no compensation package.
In addition, the report states that Blanc is "desperate" to get back into top-flight football after two years out.
Chelsea finished fifth in the Premier League table, but ended the season with silverware after defeating Manchester United in the FA Cup final.