Rodgers was sacked after Liverpool’s 1-1 draw in the Merseyside derby on Sunday.
Di Matteo was in charge of Chelsea during their Champions League winning season in 2012.
He currently has no job after leaving Schalke in May.
It is thought that the club are considering an approach for the 45-year-old.
This would come as a shock to many after several reports stating that ex-Dortmund boss Jurgen Klopp has already agreed a three-year-deal at Anfield.