The Brazilian recently rejected the club's new terms as negotiations over a new deal appear to have hit a stumbling block.
The 31-year-old wants a long-term contract, while the Blues are keen on agreeing a short-term deal.
With Luiz's future in doubt, the bookies have moves to China or the US to be the defender's next destination if he leaves Stamford Bridge.
Although Luiz is also being linked with potential high-profile moves to Inter, AC Milan and Barcelona by the bookies.
But Betfair expect Luiz to remain a Chelsea player as he is odds-on at 1/3 to still be at Stamford Bridge at the start of next season.
Betfair: David Luiz to sign for by September 1st 2018
Betfair's Katie Baylis said: “Luiz is out of contract next summer and doesn’t appear to have an offer as such from Chelsea to stay on.
"But he’s already made it clear he wants to stay at Stamford Bridge and we make it odds-on at 1/3 that he will.
"He’s 9/2 to go to China and 11/1 to go to the MLS, and we can’t see him going to any other PL clubs at this stage.”
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