Pochettino was sacked by Spurs in November after five-and-a-half years in charge and this week his gardening leave came to an end, leaving other clubs free to appoint him without paying Spurs compensation .
The Argentine has long been linked with United and Real Madrid after transforming Spurs into challengers for the Premier League title and Champions League and Rose believes he will join one of the biggest clubs in the world.
"Without a doubt, without a doubt," Rose told The Lockdown Tactics podcast. "[That intensity] they all got it from Bielsa. I know Poch, he idolises Bielsa. They all got that work ethic from him."
Asked where he thinks Pochettino will go, Rose replied: "Eventually United."
Rose was a favourite of Pochettino but the left-back fell out of favour under his successor Jose Mourinho and was sent on loan to Steve Bruce's Newcastle United in January.
Having been given his Spurs debut by Harry Redknapp and played under Tim Sherwood, Rose says he is getting used to working with an English manager again.
"Even under Poch, he had a different culture to the British," Rose said. "It wasn't that he didn't understand it...you know the British like to have a drink, it was just something that he couldn't get his head around.
"He wasn't willing to compromise on that either. Even after we beat Ajax in the Champions League semi-final and it was obviously the biggest night of our careers. On the flight home we weren't allowed a drink.
"It was 'no you're training tomorrow, you're up at 9'. So it's just one of those things. British managers do different things. Foreign managers sometimes it'll take them time to adapt or for the players to adapt to them. It's something that is just one of those things in football.
"In the changing room and we went back out to the fans, for that hour I felt on top of the world. Then we got back on the plane and we were trying to have a drink and he wasn't having it. He was like 'no we've got a game on Saturday'. The night was over.
"I do fully respect what he's done but at the same time with that Champions League semi-final we'd been together since we were 22 or 23, so for me that's all I'd known for the past five or six years, you'd play and then get one day off if you're lucky and that's it, you're grafting for the rest of the week.
"So now I'm at Newcastle, you're getting two or three days off a week if you win, so I'm thinking what's going on here then? It's a shock to the system.
"We'd only get one day off if we were lucky under Poch. Even in international breaks, he'd see the ones who would go away as having a holiday because training isn't as hard with your national team. So if you weren't in the national team you were getting beasted in training.
"You'd only get Saturday or Sunday off and then you'd get somewhere like Liverpool where they're getting seven to 10 days off.
"We've been programmed a certain way in the last five or six years and going to Newcastle it's different. I've missed playing for a British manager and I'm getting used to it again."
Rose added: "Whatever I do after football without a doubt I'd want to have Pochettino's work ethic. He's obsessed with football and his way of life is so relative to football."