The report claims Abramovich thinks Luiz is the man to lead Chelsea going forward, and believes the time is right this summer to replace the 32-year-old Terry.
The decision to replace one of the club's most successful captains would be hugely controversial at Stamford Bridge due to Terry's popularity on the Chelsea terraces.
And Luiz would be a surprise choice. He's not even third choice skipper at the moment, with Frank Lampard and Petr Cech both ahead of him in the pecking order.
But the report claims Luiz is an Abramovich favourite, and with a new manager expected to come through the door at the end of the season, the Brazilian international could be captain by opening day next term.
The 26-year-old centre-back was signed from Benfica in the 2011 January transfer window, and has become a fan favourite in west London.
With the old guard on the way out - Didier Drogba left last summer, Frank Lampard is yet to agree a new contract, and John Terry has just one year left on his current deal - Abramovich is reportedly looking ahead to the next generation of Chelsea trophy challengers.
Part of that plan involved the capture of some of the world's best young players - partly achieved by the signings of Oscar and Eden Hazard last summer.
And the report claims Jose Mourinho, should he be the man to replace interim boss Rafa Benitez, wants to continue the recruitment drive with a move for Zenit St Petersburg forward Hulk.
Turkish giants Fenerbahce and Galatasaray are keeping tabs on Terry, who's struggled with injury this season. The Chelsea skipper indicated last week that he hopes to sit down to discuss a new deal at the end of the season, but he's found it difficult to win his starting place back in the team in recent weeks.