Roman Abramovich and Marina Granovskaia reportedly disagree over how to replace Frank Lampard as Chelsea manager if results do not improve.
Lampard is under pressure after a run of five defeats in eight matches and there has been speculation that he could be sacked.
Several possible replacements have been linked with the job, including Thomas Tuchel, Julian Nagelsmann and Southampton boss Ralph Hasenhuttl.
And the Daily Star Sunday have picked up on a story by ESPN claiming that club owner Abramovuch and director Granovskaia have different views over whether an interim appointment should be made or whether the club should wait until the end of the season.
Former Blues manager Avram Grant and ex-Chelsea striker Andriy Shevchenko have been touted as possible interim options should Abramovich opt to make a change now.
Lampard, meanwhile, has insisted that he can handle the pressure he is under and turn things around.
Speaking at his post-match press conference after the recent defeat against Leicester, Lampard said: “We just have to fight. I’m not the only manager to be put under this sort of pressure.
“The lucky thing for me is that I’m good at handling pressure. I could sense that these periods would come.
“That’s all I have to concern myself with – how to deal with this and get us out of it.”