The former England midfielder tips his old club to begin a period of dominance in European football, praising its infrastructure and warning that only complacency can stop it
The 32-year-old represented die Roten for 10 years before joining Manchester United in 2007 and won the continental prize with them, defeating Valencia in the 2001 final.
Hargreaves believes that the Bundesliga giant is at the top of the European game at present, telling the Daily Mail: "You have to say they're No.1.
"That team is as good as you'll find, with a work ethic. I'd be shocked if they didn't steamroller everything over the next few years. The only issue is complacency."
With former Barcelona boss Pep Guardiola set to take over at the Allianz Arena in the summer, the former Three Lions star feels that the Spaniard may find it difficult to follow this season's potential treble-winning exploits but that he is going to the perfect club to keep up their success.
"The infrastructure has always been there," he explained. "People asked me why Guardiola chose to go there, not Chelsea. Well, he's a smart man. If Bayern is not the best-run club in Europe, you would struggle to find a better one.
"But if they win the treble, what's he going to do? It's only downhill from there. I've heard great things about Guardiola and maybe it's good that he keeps it fresh. Barcelona is the best example. They were the best team ever to play this game and to get beat as they did in the semi-final can only be down to complacency.
"Any team with success over a period can fall victim to that. We thought they were undefeatable and then to go and get beat 7-0 over two legs [by Bayern] ... it wasn't even close. It could have been 12 or 13.
"Bayern have the right balance," he added. "They're a model for a lot of people. Their stadium is probably the best in Europe, their training ground is one of the best, commercially they turn a profit and make their own money. It's done naturally.
"It's mostly [club president] Uli Hoeness who has made the club what it is. He's the heart and soul. There was a time when he said they had to decide if they had enough money to cut the trees and plants down and to go from that to where they are is pretty amazing."