The centre-back only joined the Gunners in the summer after ending his second spell at Chelsea.
Luiz penned a two-year deal at the Emirates, but was quizzed by ESPN Brasil about the possibility of heading home.
“Today, I have no such plan,” he said, as reported by Sport Witness.
“I don’t have that as a goal. But we never know, football goes very fast.
“What makes me happy is to see the quality of Brazilian football. You see Jorge Jesus with Flamengo, and the great players like Felipe, Rafinha, Gerson and Gabigol, who’s back shining as he always shone at first at Santos.
“Then you see Renato’s Gremio, who have been playing great football for many years.
“So without a doubt, I’m happy for our football. I'm glad about the ever-growing quality. [But] I’m sincere to say that today I don’t have this idea [of going home].
“I have a two-year contract with Arsenal. I have my ambitions and goals here with Arsenal, so I came here. But we never know in the future.”
Luiz left Brazilian football aged just 19 to join Benfica and has since had spells at Chelsea and PSG, winning league titles with all three clubs.
The 32-year-old has featured regularly under Unai Emery this season, making eight appearances in the Premier League and scoring one goal against Bournemouth.
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