The Germany international is on Antonio Conte's radar as he looks to bolster his defensive options.
Conte wanted a defender in the summer and moved for Rudiger - as well as Alessio Romagnoli and Kalidou Koulibaly - but eventually settled for David Luiz.
Luiz returned from PSG and has been a revelation since Conte's switch to a back three.
Chelsea have won six games in a row since the tactical move, haven't conceded a goal and have risen to the top of the league.
But the Italian is still weighing up his options and is considering a move for Rudiger, 23.
The Roma defender was quizzed on his future and asked to reassure fans that he wasn't joining Chelsea and simply said: “Next question.”
Rudiger joined Roma from Stuttgart in 2015 on loan for a season before making the move permanent last summer.
Chelsea had hoped to do a deal straight away but were knocked back despite offering just under £20m.
But the Germany defender was out injured after damaging his knee ligament and has only just returned to the side.
Roma defender Antonia Rudiger's HIGHLIGHTS
The Evening Standard report that they have now set their asking price at £30m.
Luiz has been playing with Cesar Azpilicueta and Gary Cahill in a back three and Rudiger plays in a similar formation for Roma - which could make him an even more appealing option.