However, the left-back says that he is capable of ignoring the rumours to focus solely on helping the Saints produce a strong end to the season.
"There is not a club I am not linked with, but I don't focus on that," he told Sky Sports. "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."
Shaw, whose existing deal expires in 2018, has made 29 appearances for Mauricio Pochettino's side this term.