Sarri has come under increasing pressure after a string of concerning results and performances over the last couple of months have pushed Chelsea out of the Premier League's top four.
Hazard, meanwhile, will have just 12 months left on his contract by the end of the season, potentially forcing the club to sell him if an extension cannot be agreed.
Zidane has already been rumoured as a possible option to replace Sarri should the Chelsea hierarchy decide to pull the trigger on yet another manager, and a report from The Sun now claims that the ex-Real Madrid boss has several key demands should he be hired.
A new deal for Hazard is one of them. The Chelsea number 10 is known to idolise Zidane and the potential arrive of the Frenchman could actually make those contract negotiations easier.
Secondly is a £200m transfer budget to overhaul a squad is serious need of investment. Poor recruitment - players like Danny Drinkwater and Emerson Palmieri - since last winning the Premier League in 2017 has left Chelsea playing catch up in terms of quality and depth.
That budget would even grow if it can be boosted by selling out of favour players.
Perhaps most importantly is the third condition that Zidane would have a 'major say' in recruitment alongside trusted Roman Abramovich aide and director Marina Granovskaia.
Sarri has regularly commented in recent weeks and months how little he has to do with transfers, while the continued absence of a technical director since the departure of Michael Emenalo in 2017 has seemingly left the club without a clear long-term plan.