Hoddle had been the main contender but he backed out saying that he did not have full support from the board.
Now for Sturrock - who is in charge of a second division side - to be appointed as manager, Southampton must have approached Jewell and been knocked back.
Plymouth vice-chairman Peter Jones said: "We love him; we're desperately sad to lose him if indeed we do.
"But if a man of that calibre gets the chance to pit his wits against (Arsene) Wenger and Sir Alex (Ferguson) and so forth those opportunities don't come very often.
"I think it would be difficult for any manager with real talent and real ambition to turn down the chance to manage a decent club - and let's be honest Southampton are a decent club."
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, on Sky Sports News: "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."