Pochettino was tipped as a future United target even before he was sacked as Spurs manager and has regularly been linked with the Old Trafford post since.
Rose played underneath Pochettino for Tottenham from 2014 to 2019 and the full-back, who is currently on loan at Newcastle United, believes that it is inevitable the Argentine will end up at the Red Devils.
Asked whether Pochettino was destined for a top club, Rose told the Lockdown Tactics podcast: "Without a doubt. Without a doubt. [That intensity] they all got it from [Leeds manager Marcelo] Bielsa.
"I know Poch, he idolises Bielsa. They all got that work ethic from him. Eventually United."
Pochettino, who is now free to join another club without any compensation being paid to Tottenham, has been tipped as the next Newcastle manager should their takeover be completed.