The 17-year-old defender has broken into the Saints' first team this season and has featured in the last 11 league games for Adkins' side, of which he started 10.
And while the starlet's fine performances have reportedly turned heads at the Emirates Stadium, his 47-year-old manager recently declared Shaw is not for sale - and believes he is at the right club to develop into a top player.
"No, [Wenger] didn't say anything," he told talkSPORT. "As I have said before, Luke is better playing for Southampton, 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."
Arsenal has signed two of Southampton's most promising young talents in recent years, snapping up Theo Walcott in 2006 and beating a host of rivals to the signature of Alex Oxlade-Chamberlain in 2011.
However, Adkins is firm on his stance over Shaw, and says any team who wants to take the left back away from St Mary's will face a battle from chairman Nicola Cortese.
He continued: "We have a good culture here. [Shaw] 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."
The sides drew 1-1 at St Mary's on New Year's Day, leaving Arsenal in sixth place and Southampton 17th in the Premier League table.