The 18-year-old, who is said to be a Chelsea fan, has reportedly attracted interest from the Premier League giants following an impressive season at St Mary's.
While Shaw appears to be happy about the speculation, the England international has reiterated that he is in no rush to leave Southampton.
"It's a good thing to be linked with them, but I don't concentrate on that, I've got football to focus on," The Metro quotes Shaw as saying.
"Yeah of course [I'd be happy to stay at Southampton], I've said it a number of times. It's a great club and I'm still young and have a lot to learn."
Shaw has been rewarded for his performances this season by earning a spot in the PFA Team of the Year alongside teammate Adam Lallana, who has also been linked with a move away from Southampton this summer.