The Gunners have been heavily linked with the teenage defender, who has made an impressive start to life in the Premier League.
It has been rumoured that Arsene Wenger has outlined Shaw as one of his top January transfer targets, but Adkins is adamant that his young star will not be leaving the club:
“I’ve not read any of the newspapers,” he is quoted by The Mirror.
“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.”
Arsenal have a history of signing promising young players from Southampton, with bot Theo Walcott and Alex Oxlade-Chamberlain swapping the South Coast for North London in recent years.
Walcott was snapped up by the Gunners during 2006, after a handful of impressive displays in the club’s first-team.
After being suitably impressed by the striker, Wenger returned for Oxlade-Chamberlain in 2011, paying £12m for the youngster.