Adams, who only took up the reigns at Vale Park last month, is rumoured to be seen as a potential replacement for departing Saints chief Mark Wotte by Markus Liebherr, the head of the consortium that has taken control of the South Coast club.
However, the former Leicester boss, who made 174 appearances for Southampton between 1989 and 1994, insists he is committed to his job in the Potteries.
He told The Sentinel: "Whenever the Southampton job comes up I'm invariably linked with it, being a former player. I had great times down there as a player, my family still lives down there and so I'm always getting linked with it.
"But I'm happy here at Port Vale. Would I walk out on Port Vale to take on the Southampton job? No.
"I'm an honourable man. This is a project I took on board and I'll give it my best shot."