The 43-year-old has shone as Salop chief since his appointment last year, escaping relegation from League One last season and guiding them to the top of the table 16 games into the current campaign.
His name is one of several that has been mentioned in relation to the Black Cats job, after they sacked Simon Grayson on Tuesday night.
"I've been made aware of that, I've been let know," said Hurst, after social media speculation on him being interested in the role.
"I take it as a compliment. If you are bottom of the league, I am sure you wouldn't even be linked with it."
Shrewsbury take on non-league Aldershot Town in the FA Cup first round on Saturday.
Hurst's says his focus is purely on that game and said: "I have got a job to do here.
"I've stressed the importance of the Aldershot game and I don't want anything to take away from that.
"The players have had a little bit of fun with it but the focus is on the game and getting through.
"I'm enjoying the job here and we have a lot of hard work in front of us."
On if there has been any communication with Sunderland officials, Hurst added: "No, not to my knowledge anyway.
"I'm ambitious, I want to manage as high as possible.
"But you can't help speculation. It's very much mind on the job in hand and hopefully getting through to the second round."
