Although Glenn Hoddle is believed to be the controversial first choice of Saints chairman Rupert Lowe, Football League managers Jewell, Paul Sturrock and Iain Dowie remain in the frame.
But Jewell insists he takes no notice of speculation and is putting all his energy into Latics' push for the Premiership.
He said: "I don't know about this and I think Rupert the Bear is probably a bigger admirer of me than Rupert Lowe.
"Seriously, though, I enjoy being manager of Wigan and enjoy working with the players here.
"I don't give speculation a second thought.
"I'm always going on about the players keeping focused, so if I lost my focus, that would rub off on them.
"My job is to get a result at Stoke on Saturday and until someone rings me to say I'm going or I can go, I will continue my job here because I enjoy it."
Jewell signed a three-year contract at Latics last summer and points to the loyalty he has shown throughout his career.
"I have only broken one contract in my life as a player or manager," he said.
"That was a Bradford after we stayed in the Premier League when I felt the job was getting impossible because I couldn't work with the chairman.
"I can never be accused of being disloyal, and I could have left Bradford once or twice as a player, but I didn't, it's not my style.
"I'm happy and settled here at Wigan but that doesn't mean to say I'm not ambitious – I'm fiercely ambitious.
"The chairman can match my ambition here and hopefully we can move further forward."
Jewell's name was first linked with Southampton in November, shortly after Strachan announced his intention to quit at the end of the season.
And the speculation surfaced again yesterday now Strachan has gone early and with Saints fans fiercely opposed to a return to the club for Hoddle.
A more pressing concern for Jewell is the fitness of Jimmy Bullard ahead of the visit to Stoke.
The midfielder is suffering from an infected heel and missed training yesterday to have treatment.
It's a been a rare sight to see Bullard anywhere near the physio's room – he has been an ever present in the team since signing from Peterborough just over a year ago.
Jewell said: "He's got a cut on his heel which is infected but hopefully it will clear up in a day or two.
"Hopefully there won't be a problem about him playing on Saturday and he should be back training soon."
Another player to have missed training is Steve McMillan who suffered a dead leg in a reserve game last week.
But Jewell thinks he should be available at the Britannia Stadium where he is due to take the place of the suspended Leighton Baines.
Source: Wigan Evening Post.