The 28-year-old is out of contract at the end of this season.
Bayern Munich and Juventus, who have a reputation for snapping up top-class players on free transfers, are both keen on his services.
The two clubs are understood to have a huge pay packet waiting once negotiations with foreign clubs begin in January.
Rudiger is keeping his options open after being offered a new contract by Chelsea worth just £130,000-a-week.
Striker Romelu Lukaku, the same age as the German centre-back, is currently being paid £350,000-a-week.
After helping Chelsea lift the Champions League trophy with the best defence in the competition, the club offered the deal to his representatives with a deadline of the end of the summer to agree.
Rudiger’s camp stood their ground and are now ready to listen to offers directly from rival European clubs.
