The Australian agreed on an early parting of ways with McLaren this year after the partnership had failed to deliver the results that were expected.
After weighing up his options for 2023, Ricciardo eventually agreed to become Red Bull's third driver for next season as he eyes a full-time return to racing in 2024.
And while some have questioned whether Ricciardo has taken the best route to keep himself in the limelight, McLaren CEO Brown believes that it could offer him an immediate chance to show he still has what it takes to win in F1.
He cites the example of former Mercedes reserve Nyck de Vries, who did such a good job as stand-in for Alex Albon at Williams at the Italian GP that he landed a race seat at AlphaTauri for 2023.
"Look at what happened with Nyck with one good session," said Brown. "All of a sudden he became hot property.
"So if one of those guys [at Red Bull] couldn't race for some reason, and he [Ricciardo] hopped in and all of a sudden he took that car to where it is now, it can just turn on a dime."
Asked by Autosport if the chance of a Red Bull outing was better for his prospect than having taken up a full-time seat with Haas, Brown said: "It's hard to tell. In one sense if you go to Haas and then you give it to [Kevin] Magnussen that's one way to kind of get back on the radar.
"The other is a [Red Bull] driver gets COVID, you're in a race-winning car, you go out to win the race, and you're back on the grid. So I think it's hard to say which will create the best opportunity."
Brown said he was taken aback that Ricciardo was not snapped up by other teams once it became clear after the summer break that he was available.
"I'm surprised some of the other teams that looked for drivers didn't select him," he said. "But also I think there were certain teams he wasn't interested in driving for. So maybe they would have selected him.
"But he clearly wants to stay in the game. He won Monza last year; eight races is a lot of races to win. So it's in there, we just weren't able to unlock it. And hopefully in another environment, something will unlock it, because I think we'd like to see Daniel on the grid."
