The Shrews, bottom of League One, sacked Micky Mellon two weeks ago and made an inquiry about Archibald on Wednesday having been impressed by his track record of keeping Thistle in the Premiership.
However, the Firhill manager has not spoken to Shrewsbury and gave a clear indication that, while flattered, would prefer to get on with the job of lifting the Jags away from the danger area.
Archibald said: “I’ve been here for half of my life, and I’m not going anywhere, I’ll be here on Saturday and hopefully I’m here to the end of the season and we’re still in the league.
“I’m flattered there is a bit of interest. I haven’t spoken to them and my full concentration is on Saturday’s Ross County game.
“The timing of it is a bit strange because we are second bottom of the league right now and my job is to get us out of the trouble we are in at the moment,
“There is a bit of surprise because you don’t expect anyone to come calling given the position we are in, but we’ll take that as a compliment.
“I didn’t speak to them, I don’t know a lot about them, so I would cross that bridge when I come to it. It would be a massive wrench to leave Thistle. I’ve spent 19 years here I think.”
Archibald, who took over from Jackie McNamara in February 2013, said: “I would like to manage in England at some point, it’s something different. There will come a point when Thistle fans will have had enough of me as well – that’s how football works.
“I’m not going to hide that fact, but there’s pressure on me in this job.”