But with the club apparently unable to use its entire salary cap allocation because of financial constraints and other NRL teams such as St George Illawarra reportedly interested in Henry's services, whether he will accept the Titans' offer is debatable.
Cartwright conceded coaching the Titans came with unique challenges.
"There's a lot of clubs with a lot of resources and cash and they're making it very hard to compete with," Cartwright said.
Bird believes the club's off-field woes shouldn't stop them being an attractive prospect for any coach.
He says this year's poor form has more to do with injuries and bad luck than any lack of ability within the playing group.
"We've had deficiencies this year in certain positions," Bird said.
"We've had a lot of injuries in the halves and that's definitely made our venture through the season pretty tough.
"We've got great quality back-rowers; great quality forwards; great quality outside backs.
"I don't think we can use that as an excuse that we can't keep up with the other teams."
After coming within a game of the 2010 grand final, the Titans have never fully recovered from multimillion-dollar legal disputes over a failed centre of excellence which reportedly left the club $25 million in debt.
Since then, the club has finished dead last in 2011 and failed to return to the finals, with a top-eight finish this year appearing increasingly unlikely.
Crowds are also dropping, with this year's average of 13,382 the lowest in the club's existence and attendances falling every year since a peak average of 21,618 in 2008.
Gold Coast rugby league identity Chris Close is among those claiming the Titans' problems hindered Cartwright's ability to do his job.
"Sadly, the club's had some real turmoil over the last four or five years and there's no doubt in my mind that has affected Johnny's opportunity to reach the full potential of the club and also of his own coaching career," said Close.
If Henry can be sold on taking up the Gold Coast job permanently, Titans forward Nate Myles would clearly be supportive, saying the 53-year-old has been impressive since joining the club.
"He's definitely created a bit of accountability around the group," Myles said.
"He's honest. He's always pretty spot on and the players receive that pretty good.
"He's been an asset for us. I obviously don't know whether it's going to go any further but he's been really good so far."
The issues the Titans' new coach must deal with
The squad: Veteran back-rower Ashley Harrison has retired and Luke Bailey and Mark Minichiello's futures are far from certain. Despite their age, all three leave a significant void in the club's forwards next year if they're not around.
The cash: Outgoing coach John Cartwright admits the club doesn't have the resources to match its rivals. It's hard to recruit top talent if you can't pay top wages.
The fans: Crowds are down at CBUS Super Stadium and have been declining for years. A community needs to be convinced.
The board: An ongoing internal review into the club means whoever gets appointed will need to agree with the board's plans.
The history: 2014 is looking as if it will be the fourth year without finals for the club. That record can't continue.
