The Sun claim City made the move as a result of defensive concerns.
Luiz was left out of the Chelsea side which beat Reading last night, apparently with an injury.
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.