The highly rated left-back has been linked with the likes of Manchester United and Chelsea since he burst onto the scene last season.
Shaw looked very much at home in his first Premier League campaign and the 18-year-old has also caught the eye this season.
The teenager's absence from the Southampton side that lost to Tottenham on Sunday led to further speculation that he is set to leave St Mary's.
However, Pochettino revealed the defender has a throat infection and reiterated the south-coast club's stance that Shaw will not be allowed to move on next month.
He told the club's official website: "It's pretty clear what the situation is, Luke Shaw has come out and said he doesn't want to go anywhere.
"He's very happy here and doesn't want to go anywhere else.
"I think all these rumours coming out are not positive for him and not positive for the club.
"The club's stance as well is that we don't like negotiating on something we're not interested - selling him.
"He's a very young player it is time to progress and improve and we are not willing to sell Luke Shaw."
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