Speculation over the 17-year-old's future has been rife throughout January, with Arsenal and Liverpool mooted as a potential destination.
However, Adkins insists that Southampton have no intention of selling him despite interest from some of the Barclays Premier League elite.
"We are not envisaging selling him, we're not looking to sell him," he said after the 2-1 FA Cup defeat to Manchester United.
"We don't want to sell him. "I think it is beneficial for him to be playing regularly for Southampton in the Football League, giving him a chance to develop. "
Yes, he is well courted and you can see that he has ability about him. Southampton Football Club are not looking to sell Alex Chamberlain."