The 18-year-old academy graduate has already established himself as a regular England U21 international and has been tipped for promotion to the senior England squad in the near future.
Shaw signed a new five-year contract at St Mary's and insists his future remains on the south coast.
"I don't really take notice of things that are written about me - it is frustrating at times, but I just laugh it off," he told Southampton's official matchday magazine.
"They (the media) don't know anything because they aren't around the training ground and in the dressing room with me.
"They should know that I've signed a contract at Southampton and I'm not even thinking about moving.
"I am happy at Southampton because I'm playing football, which is exactly what I want to be doing.
"There are a lot of people out there that like to twist things - especially on social media - but I've said a lot of times that I am happy here, so I'll just carry on.
"I think people are starting to realise what sort of a club Southampton is. We are young and ambitious, and we want to go places in the next couple of years."