The manager says that the 17-year-old left-back is linked with the Gunners every week, but he is under contract at St Mary's and they do not want him to leave
The Gunners are rumoured to be considering a bid for the left-back in the January transfer window, but Adkins says that they are not looking to sell.
Adkins told the Daily Mail: "I think Luke gets linked every week with Arsenal, doesn't he?"
"Luke is under contract, he is playing football for us in the Premier League, which is important.
"We are not looking to let him go anywhere. If anyone wants to come in for any of our players, by all means speak to the chairman. He does the deals and all the best with that."