The Brazilian backed his compatriot during his dispute with the Chelsea head coach last season.
After requesting to leave the club on three separate occasions, Costa was finally sold to Atletico Madrid this summer for £57m.
The defender was dropped from Chelsea’s squad for Sunday’s Premier League win over Manchester United and made to train on his own.
He was reportedly shunned for querying some of Conte’s tactics in a stormy session at their Cobham training base last Thursday.
Although Luiz was the only player to be punished and made to watch the 1-0 win over Jose Mourinho’s side from the stands at Stamford Bridge.
Willian, another close friend of Costa’s, has also had his playing time cut this season, having started only six of Chelsea’s 11 Premier League matches.
Chelsea sources insist that Conte’s treatment of Luiz is not related to Costa however.
Conte has given his players another day off today, with Luiz due back in tomorrow as he has been left out of Brazil’s squad for their friendlies against Japan and England.
The Blues are not back in Premier League action until the 18th when they take on West Brom at the Hawthorns.