The 52-year-old's last role was at Preston but, after failing to save them from relegation from the npower Championship, he was dismissed in December 11 months after taking over with the club just outside the League One play-off zone.
It was a fate which befell some of his contemporaries, with Gary Megson (Sheffield Wednesday) and Lee Clark (Huddersfield) losing their jobs while riding high in the table.
Higher up, Kenny Dalglish was sacked for finishing eighth in the Barclays Premier League with Liverpool, despite winning the Carling Cup and reaching the final of the FA Cup.
Yet Brown is still keen for a return to work and would love another chance at Hull after the recent controversial firing of Nick Barmby.
"I thought Nicky finishing eighth in his first season as manager did a very good job," Brown, speaking at The Grass Roots Football Show at the NEC in Birmingham, told Press Association Sport.
"The owners now have a responsibility to the club and the public to put someone in place they think will be the right choice.
"I would certainly be willing to sit down and talk to them.
"It is a club which is dear to my heart and a club which is on the up again, and it would be a great opportunity for someone."
Brown believes supporters are having more of a say on the future of managers, which in turn is changing the perspective of owners and chairmen.
"I was involved at Preston last season and we were in seventh or eight, three points outside of the play-offs, and I was relieved of my duties," he said.
"Gary Megson and Lee Clark also felt the wrath of the wind which is blowing through football.
"The culture we live in is that managers are not getting time and that is something I have to stomach and come to terms with one day, I hope.
"More and more supporters play a big part in getting rid of managers.
"The style of football and philosophy of the manager is now critical and you have to jump through certain hoops and appear to be a certain character.
"More and more you have opinions in the media which hype the situation, and while there is nothing wrong with opinion, at the same time it seems the manager's opinion is dropping further down the pecking order in terms of footballing decisions.
"People are demanding automatic success but it is not something I will shy away from.
"I am eager to get back in there and the experience of the last two or three years will stand me in good stead."