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The Brazilian is understood to have told the Italian he is desperate to win back his place in the Blues line-up.
But it is believed he is also ready to look for a move away from the champions next month if Conte continues to snub him.
Luiz was left out of the Chelsea squad for the home clash with Manchester United last month following a bust-up with the Italian coach.
A knee injury has kept him out of Premier League action although he did start in the Champions League victory at Qarabag on November 22.
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It is understood Luiz is now ready to return to action and this month will be pivotal in whether the 30-year-old sees his future at the club.
Former Chelsea boss Jose Mourinho is monitoring developments as are Bayern Munich.
Chelsea signed Luiz for the second time in the summer of 2016, paying Paris St-Germain £34m.