The 26-year-old Brazil international was a £21m capture from Benfica in 2011, but Mourinho reportedly has concerns over his swashbuckling style and adventurous, attacking instincts.
And with Real Madrid and Barcelona lurking, Luiz could be one of the first casualties of a Mourinho return to Chelsea.
Luiz is prone to errors, and been used as a defensive midfielder at times this season, rather than as a centre-back.
The report claims Mourinho would target a new centre-back, a holding midfielder, and at least one striker upon his return.
Players linked with Stamford Bridge in recent weeks include Liverpool target Krygiakos Papadopoulos and Real Madrid starlet Raphael Varane as Mourinho would likely revert Branislav Ivanovic to right-back.
Both Barcelona and Real Madrid will be in the market for a new defender this summer. A Mourinho-less Real Madrid are reportedly willing to sell £20m-rated Pepe rather than Varane, and Luiz has been identified as a possible replacement.
Barcelona have a problem when it comes to strength in depth. They've been forced to play Javier Mascherano and Alex Song at centre-back on occasion this term, with Carles Puyol and Gerard Pique the club's only recognised central defenders.
They reportedly have a budget of £25m for reinforcements this summer. The report claims Luiz remains a name high up on their transfer shortlist, but he's not the top target.
Paris St Germain's Thiago Silva and Manchester City's Vincent Kompany are preferred, but both are highly valued by their clubs.