The left-back has had a superb season for Saints, making his England debut and challenging Ashley Cole for a place in Roy Hodgson's World Cup squad at the age of just 18.
He was named in the PFA Premier League team of the year on Sunday evening, along with skipper Adam Lallana.
And his stellar performances up and down the left flank have seen him linked with a big money move to either Old Trafford or Stamford Bridge.
But Shaw told Sky Sports News that whilst he is flattered by the stories, he is more than happy to continue his football education on the south coast.
"It's a good thing to be linked with them, but I don't concentrate with that stuff. I've got football to focus on. That's my only thinking," he said.
"(Southampton) is a great club, I'm still young and I've got plenty to learn. It's all rumours. I'm just focusing on the two games I've got left and then see what happens."
Shaw admits he is still pinching himself, not just about playing for England, but simply becoming a regular in the Premier League.
"It's been unbelievable," he said. "For me to be 18 and to have played 30-odd games in the Premier League is something I wouldn't have even dreamed of when I was younger. And England was probably the best feeling of my life. So I'm going to keep pushing myself to become a better player."
Shaw, Lallana and strikers Rickie Lambert and Jay Rodriguez all earned call-ups to the England squad this season.
He is the latest off the famed Southampton production belt of young talent, following the likes of Theo Walcott, Gareth Bale and Alex Oxlade-Chamberlain. And Shaw says Saints fans can expect many more talented players to emerge in the next few years.
"It's not just the ones that have come through - there's plenty more to come," he said. "I've seen around the training ground, you can see the qualities they have. Southampton's a great club for youngsters - obviously myself, Callum Chambers, James Ward-Prowse... hopefully it can carry on in the future."