The 26-year-old arrived in West Yorkshire for talks with his agent and Leeds are now trying to agree a deal with the AC Milan star ahead of the deadline this Sunday.
"He's a player that we're in for but I don't want to say very much until things develop further," said Peter Reid.
"We're in negotiations and obviously things need to be tied up quickly because we're running out of time with regard to the transfer window, but we are hopeful and will just have to see how things pan out with the lad over the next couple of days."
Roque Júnior joined the European Champions in July 2000 from Brazilian club Palmeiras, and is described as a strong centre-back with a powerful and accurate tackle whilst not being afraid to take the ball upfield.
Júnior has a Portuguese passport and would therefore not require a work permit. He was part of the AC Milan side that Leeds drew 1-1 with in the San Siro in November 2000.
Meanwhile, Salomon Olembe's loan move from Marseille is expected to be completed today.
Reid said: "Danny Mills going on loan to Middlesbrough has freed up some cash and if we do that, I'm going to spend it.
"Olembe has quick feet. He plays in the middle of the park and can get about the place. If we have a few injuries and suspensions we will be down to the bare bones and he will allow me to change the formation if I want to.
"I've seen him once or twice and he's a very good player. I hope it will all be sorted out so he can figure on Saturday. I'll have a chat with him and see how he feels."