The 18-year-old left-back has been the subject of interest from the high-profile Premier League club, but Saints have "no intention" to let the defender leave the club
Chelsea & United have been long-term admirers of left-back Shaw, who has a contract at St Mary's until 2018.
The Saints underlined their resolve to hang on to Shaw - at least until the end of the season - by placing a £25 million asking price on the 18-year-old's head earlier this month in an effort to ward off interest.
But both Chelsea, who are looking for a long-term successor to Ashley Cole, and United are believed to be ready to spend around that figure in an effort to sign the player.
Pochettino, though, was resolute on Monday, telling reporters: "Southampton have no interest in selling Luke, not at this moment or in the summer.
"We have no intention of selling."
Southampton, who face Arsenal on Tuesday night, will hope that ends talk about Shaw's future as the club aim to push into the European places in the second half of the campaign.