The 17-year-old is the latest product of the Saints' academy system to generate plenty of interest, with reports suggesting the likes of Chelsea, Arsenal and Manchester City linked with a January move.
Southampton have been forced to part with the likes of Gareth Bale, Theo Walcott and Alex Oxlade-Chamberlain in the past, but a standing outside of the top flight made it almost impossible for them to block sizeable bids.
Having returned to the Premier League after a seven-year absence, the Saints are now looking to build towards a brighter future.
Shaw is very much a part of those plans and will be offered improved terms at St Mary's once he turns 18 next summer, with a three-year professional contract enough to tie him to the club for now.
Adkins is aware that interested parties may decide to test Southampton's resolve once the transfer window re-opens in the New Year, but he has made it clear that the days of having to make a profit on home-grown talent are long gone.
He said: "Luke is very happy where he is. He is in the first team, he has got great people around him and his future is very bright.
"If Southampton are in the Premier League, there is no better place for any of our young players. They have more chances of first team football here than elsewhere."