Brazil succeeded Philippe Montanier following the Frenchman's sacking on 14 January.
The 54-year-old's only game in charge to date saw him oversee the 1-0 victory over Bristol City on Saturday.
"I've been here five years. I love the football club and will do whatever they ask me to do," Brazil said.
Despite the win over the Robins, Forest are 19th in Championship table and just five points above the relegation zone.
Brazil added: "At this moment in time, I'm not aware of where the club is in terms of looking for a new manager.
"From our point of view, we're very focused on making sure we do our jobs properly. You can tell when a group of players are on board with you, and they're on board with us.
"I've been speaking to the owner about a number of things, and from my point of view he's been very supportive. We're trying very hard to bring some players in, and I'm getting very well supported by the chairman with that."
Ben Osborn, who scored the winner against Bristol City, said: "It feels like a new manager has come in and taken over."
Interim boss Gary Brazil says he would take any role at Nottingham Forest and has not ruled out accepting the manager's job on a longer-term basis.