Chelsea chiefs Roman Abramovich and Marina Granovskaia are debating over the future of manager Frank Lampard.
ESPN says Lampard's position is believed to be under threat with the Blues having won just two of their previous seven Premier League games.
The likes of Thomas Tuchel, Max Allegri and Rafael Benitez are all currently without clubs.
And Abramovich and director Marina Granovskaia are torn over who should replace Lampard if they sack him.
Southampton's Ralph Hasenhuttl and Julian Nagelsmann of RB Leipzig are also believed to be possible candidates.
The disagreement is over whether to make an interim appointment, or to wait until the end of the season.
Former Blues manager Avram Grant and ex-Chelsea striker Andriy Shevchenko are believed to be possible interim options for Abramovich and Granovskaia.
