The 21-year-old, who recently made his debut for the England Under-21 side, signed a four-year contract with the Saints a matter of weeks ago and says he has no plans to move on in the near future.
He told the Daily Echo: "I'm playing for the club I've supported all my life, but I wouldn't have signed if I didn't think the club was going forward."
Saints boss George Burley added: "Andrew is not for sale. We're in a strong position financially and Andrew is perfectly happy here, as he showed by signing his new contract.
"Premier League clubs will always look at the best young English talent in the Championship and that's what Andrew is, so we have to expect this sort of speculation.
"But I can assure all Southampton fans that Andrew won't be for sale."