League Two boss hasn't ruled out interest in being new Rotherham United manager
and live on Freeview channel 276
The 47-year-old is Rotherham’s second highest appearance maker of all time and represented the club between 1993 and 2008, playing 494 times.
He is currently enjoying a second spell at Grimsby, having led them to promotion to the Football League last season.
Hurst, who lives in Sheffield, said there has been no contact from the Millers.
But when asked directly if he could rule himself out of the job, he said: "I am here and happy (at Grimsby) and that's important to me.
“My focus is there and it is very hypothetical and there's certainly no contact that has been made. So people can just relax."
He added: “Paul has done a fantastic job over there. I think he could probably have gone a move sooner, in some regards.
“He has done a fantastic job. I know he would not have taken that decision easily and I guess (for) myself, it's an easy link.
"That's all I can say. I cannot stop any rumours or anything like that. Thankfully, I am not on social media.
"I have had quite a few messages from friends and people in football, but that's all it is. I am very focused on Swindon, I think it is going to be our toughest test of the season to date.”
Hurst would fit the profile of manager that the Millers are looking to bring in.
Chairman Tony Stewart, who is looking to finalise an appointment before the Millers’ next match with Wigan, says he will not be choosing someone from the managerial merry-go-round.
"Do we want a merry-go-round manager who goes from club to club? No,” he said.
“The first things I look for in a manager are intelligence and communication skills.
"He has to be able to communicate not just with me but with everyone else at the club. Players come from all walks of life. You can't treat them all the same.
"He has to have experience of handling players, although not necessarily as a manager. We saw how well it worked when Paul Warne stepped up from fitness coach.
"I like a young manager. Why young? Because I don't like old habits. Old habits can be bad habits."