The ex-England Under-U17 World Cup-winning boss has a huge ally in Saints' director of football operations Matt Crocker.
They worked together previously at the Football Association.
And 41-year-old Cooper is currently out of work after leaving Swansea in July.
The Welshman has ambitions to manage in the Premier League.
However, the St Mary's job would only become vacant if current boss Ralph Hasenhuttl moves on.
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