Nigel Worthington will step down as manager after the clash with Italy on Tuesday night, ending four and a half years in charge of the side.
No formal moves will be made until after the next IFA board meeting later this month, but Dowie appears interested in the post.
He has not managed since a brief and ill-fated attempt to prevent Hull from dropping out of the Barclays Premier League last year, working instead as a media pundit.
"The proudest moment of my playing career was captaining my country and I'm always happy to help and the most important thing is Northern Ireland being a successful nation," he told Sky Sports News.
"I believe my CV stands up to scrutiny and if the IFA want to have a conversation with me I would be happy to do that.
"If I can help I would. It would be a conversation I would have to have.
"I have played for Northern Ireland and I would never turn my back on them."
Dowie impressed in charge of Crystal Palace, winning an unlikely promotion to the top flight but proving unable to save them from relegation.
He went on to manage Charlton, but lasted just 15 games before being sacked. Spells at Coventry and QPR followed before brief stints at Newcastle - as part of Alan Shearer's backroom team - and Hull, where he worked as the club's football management consultant after Phil Brown's departure.
It is understood the IFA would welcome his application, while they are also likely to run the rule over Shamrock Rovers boss Michael O'Neill and his caretaker assistant Jim Magilton.
One of the men central to the decision-making process will be IFA president Jim Shaw.
He was the man Worthington offered his resignation to and he was quick to go on record with his appreciation of the former Norwich boss.
"First of all, both personally and on behalf of the association, I would like to thank Nigel for his four and a half years in charge and the good work he's done," said Shaw.
"He has done good work in maintaining continuity and developing the game in Northern Ireland. People don't always see what is going on beneath the water when the duck is floating along the surface.
"I was surprised. The guy has done a good job and he's always been above board. I always think it's a sad day when a manager goes who hasn't done anything dramatically wrong."
Asked if Worthington had any chance of earning a new contract, Shaw added: "That's a hypothetical question, the association was never intending to discuss this until the last game was over. But I'd have thought everything would have been in the pot."
Veteran goalkeeper Maik Taylor, who will start against Italy for what is likely to be a farewell appearance at the age of 40, spoke up for Worthington on behalf of the squad.
"You won't find a player with a bad word to say about Nigel," he said.
"He was always open-minded and has always looked for feedback to see where we can improve as a team.
"You know how small the pool of players is and I honestly don't think he could have done any more than he's done.
"Whoever comes in next is going to have to call on a lot of younger players to step up earlier than they may have hoped."