Pochettino is frontrunner for the Juventus job after it emerged Massimiliano Allegri is to depart.
Asked what the club need to do to continue their recent success, Rose told talkSPORT: "Listen to the manager. I fully agree with what he says. He said recently what the next chapter of the club is and I agree with him.
"Its safe to say that not many could operate in the circumstances with no stadium and not signing anybody.
"Spurs are a part of the big six and we have a different way of working and there aren't many managers that would bring in Champions League football three or four years in a row while bringing players through and getting into the England squad. Hopefully we can give him what he wants."