Manchester United, Chelsea and Manchester City are all reportedly keen to sign the 18-year-old England international, who has also been linked with Spanish giants Real Madrid.
Shaw said: "There is not a club I am not linked with, but I don't focus on that.
"My main focus is my football on the pitch and I just want to keep doing that.
"It doesn't really bother me the attention I get. I just stay focused on my game on the pitch. Whatever is said is said.
"Stuff like that is going to happen but my main priority is the games. We've still got six left, so all the focus is on that."
Southampton's owner Katharina Liebherr and her recently-formed board will sit down with manager Mauricio Pochettino at the end of the season to discuss the plans for the club going forwards.
Tying the former Argentina international down to a new contract is likely to be one of the main priorities and one which could keep the vultures, who are circling Shaw and some of the club's other leading players, away from St Mary's.
"I would say it is a big time for the club," Shaw said.
"They've got to get the manager down on a long-term contract, which will probably be the first thing they try and do.
"Then, obviously, to keep the stars that have been mentioned in the papers that have been linked with different clubs.
"This is a very important summer and if they want to push on then they are going to do things that I've just said.
"This club can push on, definitely, I think if we get our squad strengthened.
"I think in the next year or so we can be challenging the top five teams."