City manager Roberto Mancini  is desperate to land a new defender at Etihad Stadium as a defensive cover with Micah Richards injured for ten weeks.
Luiz was axed from Wednesday's win over Reading while Chelsea and City tried to thrash out a deal.
However, the Brazilian center-back claimed on Twitter he has a knee injury, and it is understood Chelsea were angered by the Tweet and Luiz has been fined.
"This social media thing is all around us now. We'll deal with it internally," The Sun quoted Blues manager Roberto Di Matteo, as saying.
Luiz is still a big part of Di Matteo's plans and City will need to significantly up their offer to prise him away.
Stylish Luiz arrived at Stamford Bridge in a 21million pound deal from Benfica in January 2011 and became an instant hit with the fans. (ANI )