The Germany international has fallen out-of-favour under Frank Lampard since the start of the season and has failed to play a single minute of first-team football.
Rudiger was an unused substitute in the season opener at Brighton & Hove Albion and he has since been left out of the matchday squad to face Liverpool and Barnsley.
Hence, there is speculation regarding his future with the Blues and Goal.com claims that Paris Saint-Germain, Barcelona and former side Roma are keeping tabs on his situation.
Les Parisiens are eyeing a low-cost option to reinforce the central defensive department after the departure of Thiago Silva on a free transfer.
Meanwhile, Roma could move for him, suppose they are unable to land Manchester United’s Chris Smalling.
Barcelona may similarly consider an approach, if they fail to negotiate a deal for Eric Garcia from Manchester City.
Rudiger recently returned to the Germany mix and he will want regular game time in order to keep his position for the European Championships next summer.
As such, a move away from Stamford Bridge seems a genuine possibility, given Thiago Silva, Kurt Zouma, Andreas Christensen and Fikayo Tomori are preferred ahead of him.
Chelsea would ideally want to sell him on a permanent deal, but it is reported that they may agree to a season-long loan with the option to buy.
Rudiger has spent the past three years with the Blues and he is apparently open to joining a Premier League rival, should the opportunity arise.
Stats from Transfermarkt.com