The in-form handler had been non-committal about sending his stable star to Australia, but the decision has now been taken to make the trip having been handed a weight of 53kg (8st 5lb).
"I think we'll go," said Jardine.
"He's got the same mark as Heartbreak City (last year's Ebor winner who finished a close second in Melbourne) and he should get a run.
"I'd be hopeful of getting him there in the same form he is in now and if he is, he must have a chance.
"He's a stayer with a change of gear, which is what you need.
"It's not every year you get the chance to run in a Melbourne Cup."
Sunday's impressive Irish St Leger winner will have to shoulder 58kg (9st 2lb), with the legendary Makybe Diva the only horse able to defy such a weight in the last 40 years.
Order Of St George also has the Prix de l'Arc de Triomphe, in which he finished third last year, as an autumn aim and his connections have some serious thinking to do.
Part-owner Lloyd Williams, who has won the Melbourne Cup five times already, believes the ground will be a big factor in the decision.
"He needs good to soft," he told www.heralsdsun.com.au.
"Obviously I would love to run him. The Melbourne Cup, to me, is everything that racing stands for in Australia - our only international event.
"But Aidan needs to select (the) best chance (based on) tracks and travel. The Arc (is) one hour away (with the) chance of rain. The Cup is 30 plus hours."
Greg Carpenter, chief handicapper in Australia, believes he has given O'Brien a carrot.
"The reason I'm so keen to see Order Of St George travel to Australia is for the last three years he's been the powerhouse of European staying," said Carpenter.
"I think that we would see a world-class stayer if he came here. It would be a challenge for him."
Godolphin's Hartnell is due to carry just 0.5kg less than Order Of St George after finishing third last year.
Other notable European-based possibles include Barsanti and Marmelo, who both have 55kg (8st 9lb), while Max Dynamite and St Michel are on 54kg (8st 7lb).
Marco Botti's Dylan Mouth is on 53.5kg (8st 6lb).