The Montgomery Waters Meadow boss was installed as one of the early bookmakers' favourite to replace Carlos Carvalhal at Hillsborough after the Portuguese was sacked.
But Hurst, who was born in Sheffield is a lifelong Owls fan, said there is nothing in the rumours and that he is fully-focused on his side's next game, a trip to Southend on Saturday.
"I know about the speculation because when the manager was sacked my wife's phone was going mad - she wondered what was going on," smiled Hurst after proudly watching his side battle to a 0-0 draw with League One leaders Wigan.
"But that's just friends that would like to see me at their hometown football club.
"It's a massive club that I would love to see in the Premier League again along with, as much as they're not my team, the other side of Sheffield because it's good for the city.
"But there's nothing in it as far as I'm concerned. I'm certainly fully-focused on going to Southend and getting another result."
Town remain second with 48 points in League One at the division's halfway stage, as well as remaining in the FA Cup and Checkatrade Trophy.
The season's success has also seen Hurst linked with Championship Sunderland in recent months.