The 18-year-old has risen to prominence with a series of superb displays for the St Mary's Stadium outfit and is being touted as a future England regular.
As exclusively revealed by Goal, Shaw's performances have attracted interest from some of the Premier League's top clubs, with Tottenham jumping ahead of Chelsea in the race to sign the teenager.
|28/1||Southampton are 28/1 with bet365 to finish in the top four|
"They can show their interest," he said. "That's not something we control. But in this individual case he is not a player we are willing to sell. In a sporting manner, he is not for sale."
Shaw's team-mate Jay Rodriguez is another Southampton player in top form this term who also harbours long-term England ambitions.
And the forward - who earned his maiden international cap in a 2-0 friendly defeat to Chile in November - has set his sights on a spot at the World Cup in Brazil next year.
"Obviously I wasn't happy with my performance in the [Chile] game," he commented. "But the experience was unbelievable for me.
"I took a lot of positives from that, but I would have obviously liked it to have gone better and to get the win. It would be a great feeling to go to a World Cup, but I have a lot of hard work to do.
"I need to keep trying to improve as a player for Southampton."