Orlando Pirates are also interested in the New Zealand international, but the Brazilians look to have the inside track on finally landing their long-time target.
According to a source close to the Brazilians, the club is pushing to sign Brockie in time to beat the January 15 registration deadline for CAF competition.
"There has been progress in terms of negotiations. Everything is looking positive," said the source.
"Brockie could be announced a Sundowns player this week."
Meanwhile, SuperSport coach Eric Tinkler was dismissive when asked about Brockie's future following his side's goalless draw with Kaizer Chiefs at Mbombela Stadium on Saturday.
"We've heard that Sundowns have had an interest in Brockie that's existed in the last six months, but as yet we haven't received any offer," Tinkler said.
He added: "No player is not for sale, every player has a price. We are not going to be giving players away for free, that's for sure. If you're a professional player then you should know that you are contracted to the club. You need to behave as a professional player. You need to keep working, it's as simple as that."
Asked if Matsatsantsa will go into the market if Brockie leaves, Tinkler said: "In the event he leaves then obviously we have to go into the market because if you lose one you have to replace one, it's as simple as that.
"We have a 28-man squad, that's what we work with. Right now we have a 28-man squad, so we are not looking to sign anyone. The minute we lose players then we sign, it's as simple as that."