Although that offer was rejected by Chelsea, it was reportedly enough to convince Luiz to speak to Mourinho and make his wishes clear just a few days before the start of the new Premier League season.
The report also states that:
Luiz's stance has encouraged Barca, who are now prepared to raise their offer to around £31m. That, however, falls £12m short of Chelsea's minimum expectation.
If Chelsea are indeed demanding £43 million for the former Benfica defender, it would leave them with a healthy profit of almost £22 million on the £21.3 million they paid in January 2011.
The Catalan giants have been linked with a move for Luiz since Pep Guardiola was in charge and it appears that new boss, Gerardo Martino, is even more keen on adding the defender to his ranks.
Martino has made central defence his priority with a couple of weeks before the transfer window closes and recently drew up a list of potential targets, of which Luiz was top.
Mourinho now has two options. He can either cash in on the talented defender and use the proceeds to buy a replacement, or he and owner Roman Abramovich can decide not to sell no matter what the Spanish side offers.
A regular in the heart of Chelsea's back four last season, Luiz has also forced his way into Brazil's starting XI and starred in his country's summer success at the Confederations Cup.
He has eliminated many of the comedic mistakes that blighted his first season at Stamford Bridge and matured into a reliable, gifted defender.
He has also proved his versatility by relishing a deep-lying midfield role under Rafa Benitez last season, a position where his eye for a pass and attacking instincts were utilised effectively.
Mourinho has indicated that he sees Luiz as a vital part of his plans for next season. The Sun quote the Portuguese boss as saying:
I like central defenders to be able to play. Again, it is a question of making the right decision.
For David Luiz, that is the important thing—to make the right decision.
But when a player is different and has more potential than others, he has to use his talent in a good way.
But the former Real Madrid boss will not be content to keep a player who has his heart set on a move elsewhere.
The Special One built his first Chelsea revolution on team spirit and belief, and he will not want Luiz disrupting the finely-tuned harmony within his squad.
Although he rates Luiz highly, Mourinho will have no problem selling him if Barcelona meet Chelsea's inflated asking price.
If they do, Mourinho will have the funds to rebuild his defence and improve his bid for long-term target Wayne Rooney. But if not, he will still have one of the world's best central defenders at his disposal.
Much like his home record during his first stint at Chelsea, Mourinho cannot lose.