The Hampshire club sacked boss Dean Holdsworth on Wednesday night having taken just seven points from their last seven matches, with Town sitting 20th in npower League Two, three places and two points above the relegation zone.
Scott is leading the early running, priced as low as 1/3 by one bookmaker, and has been without a post for almost a year following his dismissal by Rotherham.
"I'm out of work and I want to work, I want to get going again," Scott told Press Association Sport. "It's a local-ish club to me, so yes it's something I'd be interested in, definitely. But there's several clubs looking for managers at the moment, so we'll see what happens."
He added: "I don't look at who's favourite and who's in the running because I'm not the one making decisions on things."
Scott guided Brentford from League Two strugglers to 2008/09 title winners in the space of 18 months before securing a ninth-placed finish in League One the following season, only to be sacked in February 2011 with the Bees struggling at the wrong end of the table.
He duly took the reins at Rotherham in April of that year but lasted less than 12 months before being given the boot with the Millers adrift of the play-off places in League Two.
Asked whether the Shots' lowly league position would make the job a daunting one, Scott replied: "As a manager out of work you've got to look at the whole picture and believe in yourself.
"When I took over at Brentford we were struggling down the bottom of League Two and managed to finish mid-table. I'm not daunted by any task no matter what club it is and what situation they're in. I believe in myself and the way I manage. I think that's the way you've got to be."
Aldershot are hopeful of making an appointment before Saturday's home clash against Fleetwood, with the likes of former Shots boss Gary Waddock as well as Graham Westley and Paul Buckle also linked.