The 17-year-old has been held in high regard at St Mary’s for some time and has begun to breakthrough into their first-team, making 13 appearances this season.
Arsenal, who are looking to strengthen in that area as they try and offload Andre Santos, are said to be keen on signing the hot prospect.
But Adkins has denied reports he’s spoken to his opposite number, insisting that Shaw should remain with the Saints as he starts his footballing career.
"No, [Wenger] didn't say anything,” he said. "As I have said before, Luke is better playing for Southampton Football Club, where he is being nurtured and looked after.
"He is still only 17 and playing in the Premier League, where he is getting an opportunity to flourish, to make some mistakes and to keep kicking on.
"We have a good culture here. He is under contract. We are not looking to let him go.
"This is best place for him at this point in his career. He has a big, big future in the game, which he demonstrated with his performance against Arsenal the other night.
"If anyone wants to try and do business, all the best dealing with the chairman."