The Germany international is one of a number of Roma players being linked with a move away from the Italian capital this summer.
Rudiger scored two goals in 30 Serie A appearances for Roma this term after establishing himself as a first-choice centre-half alongside Kostas Manolas.
According to Il Tempo, Roma coule be open to selling Rudiger in order to keep some of their bigger names stars such as Manolas, Miralem Pjanic and Radja Nainggolan.
Chelsea have appointed Antonio Conte as their permanent manager after Jose Mourinho was sacked and replaced by Guus Hiddink on a temporary last year.
The Blues finished in ninth place in the Premier League table following a dismal defence of their top-flight crown.
Roma finished 11 points behind Serie A champions Juventus after an enthralling title race.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news