The 18-year-old left-back has emerged as one of the best young talents in the Premier League, and reports have linked the Saints teenager with a £25m move this month.
But Pochettino has confirmed that Southampton have absolutely no desire to entertain offers for the 18-year-old.
"Southampton has no interest in selling him - not at this moment or in the summer," Pochettino was quoted as saying by talkSPORT.
"We have no intention."
Shaw penned a five-year contract with Southampton upon turning 18 last July, and the England under-21 international has become an integral part of the club's defence this season.
He's been tipped for full national team honours soon enough. But despite interest from some of the biggest teams in the division, Shaw has remained focussed on his performances for the south-coast side.
United and Chelsea have long-term concerns at left-back, with United's 32-year-old full-back Patrice Evra out of contract at Old Trafford at the end of the season.
And Chelsea's 33-year-old Ashley Cole has been in and out of the team under Jose Mourinho this campaign.