The Brazilian has been linked with a move to Manchester United in the past but the Red Devils were unable to agree a fee with the Italian club.
Anderson changed his agent recently and is now represented by Giuliano Bertolucci, who has close ties with new Chelsea boss Antonio Conte.
And, according to Gazzetta dello Sport, Conte has been in contact with both Anderson and his agent about a potential switch to Stamford Bridge.
Lazio were determined to keep hold of Anderson earlier in the summer but the 23-year-old has apparently fallen out with manager Simone Inzaghi about participating for Brazil in the upcoming Olympics.
Conte has reportedly told Anderson he will allow him to travel to Rio if he signs for Chelsea and further talks are expected to take place this week.