According to the 'Corriere dello Sport', Blanc's entourage were in Rome for the game against Juventus with the idea of offering the ex-PSG coach's services to the Italian side.
The Frenchman, who has been unemployed since he left PSG in 2016, is the current favourite to take over from Ranieri at the Stadio Olimpico.
However, it is not currently known if Roma themselves are interested in the former French national manager as they look to close the gap on perennial champions Juventus.
Other names linked with the job include Rafael Benitez, Antonio Conte and Maurizio Sarri, although it seems the latter will be staying at Chelsea after a positive end to the season.