The Sun says there are growing fears the next owner must move fast amid fears in the dressing room the squad which won the Champions League is breaking up with rumours N'Golo Kante and Jorginho could go.
Some Chelsea stars are not buying the explanation that sanctions imposed on Russian Abramovich prevented a deal being struck with the inspirational German centre half.
They instead believe the club should have had one of the cornerstones of the dressing room tied down for the future long before the war in Ukraine kicked off in late February.
Chelsea offered Rudiger a substantial deal to stay but it wasn't enough to persuade him to sign an extension to his contract which expires in just a few weeks' time.
In particular midfield pair Kante and Jorginho are about to enter the final year of their contracts.
Insiders at Stamford Bridge also believe the festering uncertainty among the playing staff is behind the team's unconvincing displays in recent games.