The 18-year-old academy graduate is considered one of the brightest prospects in the Premier League and has been tipped as a future England international.
Shaw's growing profile has seen speculation mount over his future, despite the England Under-21 international penning a five-year deal at St Mary's in the summer.
United and Chelsea are being regularly linked but the teenage left-back 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," Shaw 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."