Oxlade-Chamberlain signed his first professional deal with Saints in August on his 17th birthday.
"He's a talent, he's one for the future, and I'm sure he's going to be courted by a lot of football clubs," Adkins told BBC Radio Solent.
"He's our player, we're bringing him through, and he's part of the future at this club. We're trying to nurture him as best we can, while also allowing him to play games of football and flourish."
"We haven't looked to sell Alex, or any of our players for that matter. There certainly haven't been any bids."
Oxlade-Chamberlain is the son of former England winger Mark Chamberlain, and Adkins knows that will help the player in the long run.
"We've sat down with Alex and his family because we realised early on that he might ultimately be linked with big football clubs. His family are very supportive, and we're all singing off the same hymn-sheet."
Source: BBC Sport
Source: BBC Sport