The 17-year-old has been constantly linked with a move to one of the Barclays Premier League giants, with recent reports suggesting a move to the Gunners was all-but secured.
However, Adkins has denied such speculation and told Sky Sports News: "We had the same sort of scenario in January. He was going to go in January, wasn't he? But he didn't. I think it will be interesting when does that materialise if Arsenal or whoever does start talking to the football club.
"At this moment in time he is at Solent University doing fitness testing with the players and I had a conversation with Alex last week, he was doing a little bit of training. He really loves being at Southampton. It is as simple as that."
He added: "I think probably there is conversation going on in the boardroom at Arsenal about players who are probably going to leave and players that are going to leave.
"If Arsenal wanted to put a bid in I am sure they would put a bid in the right manner to the board and then this football club will decide what they want to go and do with that bad if it is offered."