Sturrock, 47, a former Scotland team-mate of Strachan, has held talks with Saints chairman Rupert Lowe and is set to move to St Mary's as soon as Lowe and Argyle vice-chairman Peter Jones agree on compensation.
Sturrock was catapulted to the front of a queue of managers reported to include sacked Marseille manager Alain Perrin, Qatar coach Phillipe Troussier and Leicester boss Micky Adams by Hoddle's decision to tear up his application to win his old job back.
The ex England coach, who walked out on Saints in Match 2001 to take the Tottenham job, was Lowe's preferred choice. But the Southampton supremo could not guarantee Hoddle the full support of his seven-man board of directors a position the manager said would be "untenable."
Hoddle said: "It's clear there was a great deal of support for me on the board but it wasn't 100%. Therefore I've reluctantly withdrawn my name from consideration for the post."
Hoddle's shock move is set to hand Sturrock, who has hauled Plymouth from the foot of the Third Division to the top of Division Two, his first crack at Premiership management in England.
The former Dundee United chief signed a new five-year contract at Home Park in the summer but, crucially, insisted on a get-out clause which allowed him to speak to Lowe.
Argyle vice-chairman Peter Jones said: "We're talking about compensation and it looks very much that he'll be the next Southampton manager. He's at the top of their list and we're of the view that if any employee's heart goes out of being here, you have to look forward.
"We're top of our league, have 12 games to go and don't want the last quarter of our season to be polluted by this. We basically want to get on with things. I know Southampton want to get on with it as well so I wouldn't be surprised if something is sorted out very soon."
Jones added: "It's not cut and dried yet. Paul's contracted until 2008 and we really feel we deserve to be compensated for the loss of him.
"We absolutely love the man. He's brilliant but it would be difficult for any manager with ambition to turn down the chance to manage at the highest level."
So, assuming compensation is finalised, and for a club with Southampton's top-flight resources that will not be a problem, Sturrock is likely to assume the St Mary's hot-seat in the immediate future and certainly before their next game, next Sunday's home date with Liverpool.
Lowe has been reluctant to shed any light on his recruitment plans, a stubbornness which has only fanned the uncertainty since Strachan first announced he was leaving at the end of the season and then departed ahead of time last month.
The Saints chairman is poised to appoint his second Scot on the trot but reverted to type today when quizzed on Sturrock, snapping: "We don't comment on any speculation.
"When we've a made a decision, we'll let everyone know."
Sturrock steered Plymouth to mid-table respectability in his first season and Division Three championship in the 2001-02 term.