The Brazilian's future will depend a lot on Antonio Conte and whether he remains at the club, with Luiz likely to want to leave if the former Juventus head coach remains in charge at Stamford Bridge.
And any decision over the 31-year-old will be put on hold until the managerial situation is resolved, with Chelsea having not yet received a formal offer for the centre-back.
Luiz has played just 17 times this season having been dropped for Andreas Christensen, while he has also struggled with injury and needed regular treatment for a recurring knee problem.
Monaco signed Chelsea's technical director Michael Emenalo in November and it is those links with his former employer that will likely help in the Ligue 1 side's pursuit of Luiz, and another potential targets from the Blues.
Chelsea re-signed Luiz from Paris Saint-Germain for £32 million on transfer deadline day in August 2016 and he remains a hugely respected figure in both the dressing room and among the higher-ups at the club.
Luiz invited the Chelsea first team to his fancy dress party on Monday to celebrate his 31st birthday although Conte appeared not to receive an invite, insisting he doesn't like parties .
The Blues are still in with a chance of securing their place in next season's Champions League and boosted those hopes with Saturday's 1-0 win over Swansea.