The 62-year-old is without a club after spending the back end of last season at Barrow, who he helped guide to safety in League Two and who are now managed by ex-Town boss Pete Wild.
"I wouldn't be turning a blind eye to it, that's for sure," Brown said when asked if he would be interested in the Halifax job.
"I've got an affinity with Halifax, I've got an affinity with a lot of clubs.
"I was buoyed by the reception when we came back with Southend. The people that knew me before were still there strangely enough, so there's a lot of continuity at the club.
"The club seems very stable and, yes, it's something I would listen to, absolutely."
On whether he would be applying for the vacancy, Brown said: "Yeah, I will probably put my name in the hat, for sure.
"There is a number of options out there at the moment.
"It's one of those times where the merry-go-round has well and truly started, for sure.
"It's certainly something I would consider."
When asked what would attract him to the Halifax job, Brown said: "The challenge of getting them out of probably the toughest division I think.
"Having managed in all five divisions, I did find it a different type of challenge.
"It wasn't a different style of football, it was just a different type of challenge.
"Sunderland, my team ,has just been promoted from League One to the Championship, having wallowed in League One for four years. They've lost a couple of managers en route, but managed to do it this year.
"But getting promoted from the National League back into the EFL is probably one of the toughest challenges.
"I've done it from the second to the first, I've done it from the Championship to the Premier League on three separate occasions.
"I'm not saying that was easy by any stretch of the imagination, but to go from the National League, where half if not more of the teams have got experience of a higher level, I think it's an unbelievable challenge."
Brown made 165 appearances over three seasons for Halifax between 1985 and 1988, winning the supporters' player of the year and earning a place in the PFA Fourth Division team of the year in his final season at the club.
"Home is where the heart is, at the time I had a fantastic time. From a footballing perspective it got me on the map, got me on the road to bigger and better things if you like," Brown said.
"It was part of a good journey and a successful journey in my life. I've got great memories of Halifax.
"I thought the club looked like a professional outfit, what I mean by that is they conducted themselves in the right way.
"A lot of teams in the National League get relegated into it and then become non-league.
"I've just left Barrow and there's an air of non-league about them, that they have to try desperately to shed as part of your DNA, your make-up. I didn't get that feeling at Halifax, there's no doubt for me it's a professional football club and it deserves its crack at the promotion campaign they'll be building next year."
Asked if he felt his recent experience managing in the fifth tier was in his favour, Brown said: "To a certain extent, but having managed in the National League with Southend it was the wrong club at the wrong time.
"I brought together a team that was wallowing in Division Two and when we left them we were knocking at the door of the Championship.
"But when I went back to Southend, it was certainly a club in massive decline, they'd had probably four or five managers in between me and then me coming back, and because of that it all sorts of issues and problems, and one of them was the fact that it was dysfunctional.
"I don't think if I walked into Halifax Town I'd be walking into a dysfunctional club. If you ask Pete Wild about it, it certainly looked like a club on the up, and if it's on the up there's only one place to go, and that's back into the Football League."
Brown left Southend last season with the club just above the relegation zone.
He was reappointed at Roots Hall towards the end of the previous season, tasked with trying to keep them in League Two.
After leaving Southend, he was appointed Barrow manager and successfully guided them to safety in League Two.
Negotiations then broke down over him staying on permanently at Holker Street, with former Halifax boss Pete Wild being appointed there today (Friday).
Brown is most famous as a manager for guiding Hull City into the Premier League in 2008 and then keeping The Tigers in the top flight the following season.
His first full-time management job was at Derby, prior to Hull, after which he also took charge of Preston, Swindon and Hyderabad in India as well as his two stints at Southend.
"There's no doubt in my mind where I'm at, the experience I've got, but it counts for nothing unless you surround yourself with successful people as well," Brown said.
"I don't just mean players, I think a football club is all about the people that run the show behind the scenes, not just about chairmen and boardrooms, it's about people that run the place, I think that's the most important part.
"I got that vibe from Halifax when I came to the club, having not been there for 20-odd years, it's still that friendly atmosphere and still that vibe about the place that it felt a homely club, and I've always thought that about Halifax Town."
On what he felt he could bring to the club should he be appointed, Brown said: "I noticed the demand for good football, which was always a thing that I had as a player under Mick Jones and Billy Ayre, they demanded good football, they demanded winning football, they demanded a style of play that would get bums on seats.
"I think Pete Wild achieved that to a certain extent, hence the reason why he's got his opportunity at a club in the Football League.
"I'd be buoyed by the fact that I know what's possible at Halifax, you can build something and get a lot of support from the Yorkshire people getting behind the club.
"Yeah, it would be an exciting prospect."