PSG are currently weighing him up as a low-cost option on a limited budget in this transfer window, while Roma could look to him as an alternative to Chris Smalling.
Barcelona are reluctant to make an offer for Rudiger as they prioritise Manchester City youngster Eric Garcia, however he is an option.
Rudiger would welcome offers from big Premier League clubs after he and his wife started a family during the last season, and he was surprised be out of the reckoning at Chelsea as the season began.
Frank Lampard hasn't dropped Rudiger due to personal problems - he has simply opted to offload the defender for sporting reasons following the signing of Thiago Silva from PSG.
"There are lots of rumours about those players and others too, so every player would always be a case-by-case situation, and one that would be a happy solution for the player, for myself and the club," Lampard said ahead of the away trip to West Brom.
"Yes, we have a big squad we know that, but at the moment the players remain ours and we'll see how things go as the time goes on."
Chelsea are hoping to sell the defender in the transfer window but may have to settle on loaning him, with an option or obligation to buy the Germany international permanently being part of the deal.
Rudiger is sad about being sidelined, but he is now trying to keep his Germany spot secure for the upcoming European Championships in 2021.
Tomori could start against West Brom, with Andreas Christensen suspended following his red card against Liverpool last weekend. Silva, meanwhile, completed 60 minutes against Barnsley in his bid to earn fitness after playing in the Champions League final defeat to Bayern just over a month ago.