The Catalan giants are long-term admirers of the 26-year-old stopper, who played a starring role for Brazil during the recently concluded Confederations Cup, which Brazil won having beaten Spain 3-0 in the final.
Suitably impressed by Luiz's performances, Barcelona have finally firmed up their interest by launching an official bid for the former Benfica ace.
But Chelsea boss Jose Mourinho is adamant that Luiz will not be sold and is determined to keep hold of the sought-after talent.
Speaking after his side's 2-0 pre-season win over AC Milan, Mourinho said: "David has come back with us fantastically and we have to use his quality.
"He has big self-confidence and self-esteem, especially when he comes up from the back with the ball."
Luiz has been the subject of intense transfer speculation all summer, with Manchester United and Bayern Munich previously linked with a big-money move.
However Luiz, who signed a five-year deal with Chelsea last summer, is central to Mourinho's plans and the Portuguese tactician is desperate to ward off potential suitors.
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