Luiz was strongly linked with the Spanish giants in the summer but a deal failed to materialise, with some reports claiming this was due to Chelsea's valuation of the 26-year-old.
However, Barcelona are said to be preparing a new bid for the eccentric Brazil centre-back, while European champions Bayern Munich are also reportedly interested.
Luiz, who is fit again following a knee injury, has only made five appearances under Mourinho this season but will partner John Terry against Crystal Palace on Saturday to allow Gary Cahill to rest a quadriceps problem.
"Everything is clear. He's our player and we are happy he's back in a moment when we need him and John in defence," said Mourinho.
"The market is open in January but I don't think we will be buying or selling. There has been no contact from other clubs or from his people."
England left back Ashley Cole, who was left out by Mourinho for a run of games before starting Wednesday's 1-0 UEFA Champions League win against Steaua Bucharest alongside Luiz, will make way on Saturday for Cesar Azpilicueta.
"I need the team to change again. I need fresh players. I need Ashley to be fresh for Sunderland," Mourinho said.
Chelsea are midway through a testing run of nine games in December, including a Capital One Cup quarter-final at Sunderland on Tuesday and Premier League games at leaders Arsenal and at home to second-placed Liverpool either side of Christmas.
"It's important not to kill players by playing them every minute of every game," Mourinho said.
"I won't risk any players so Cahill for example is not involved, to protect a little pain he's feeling in his quadriceps."