Brawn knows all about Formula One domination, having worked with Michael Schumacher through a golden period at Ferrari and then winning titles with his own eponymous team in 2009 before getting Mercedes started on the road to unprecedented success.
Speaking ahead of the British launch on Wednesday of the four-part series Brawn: The Impossible Formula 1 Story on Disney+, the former F1 managing director and ex-Ferrari technical director saw McLaren as a team to watch.
"They've clearly got a much stronger organisation now. Hats off to (team principal) Andrea Stella. He was one of my engineers at Ferrari. And I guess you don't see these little tiger cubs growing up to be big tigers," he said.
"I'm really pleased how well he's doing and he seems to have galvanised the organisation. So, I think with that improvement going into next season they can be a real threat.
"They’ve got fantastic drivers as well, pushing each other very hard."
Britain's Lando Norris (23) has finished second six times in 20 races while Australian rookie teammate Oscar Piastri (22) won the Qatar Saturday sprint and finished second to Verstappen in the Sunday grand prix with Norris third.
After failing to score in their first two races of the campaign, McLaren have staged an impressive recovery and are now fourth overall.
Brawn was also optimistic Ferrari would improve under Fred Vasseur's guidance but recognised Red Bull would not be standing still and had the added benefit of being able to switch attention early to next year's car.
Red Bull have so far won 19 of 20 races, with Verstappen triumphant 17 times - a record for a single season that he can extend in Las Vegas this weekend - and teammate Sergio Perez (33) twice.
"It's been a bit frustrating. I think sometimes when you get a team dominating you'd hope that both drivers would be fighting each other and that hasn't happened with Red Bull, which is a shame," said Brawn.
