The Welshman is entered in the specialty event Saturday at the Hershey Canadian Indoor Open Championships. The field includes Luguelin Santos of the Dominican Republic, the 400-metre silver medallist at the 2012 Olympics.
They are aiming at the indoor 600-metre mark of one minute 15.12 seconds set in 1999 in Germany by Nico Motchebon.
"I've trained hard all winter and prepped really well," Greene said Tuesday trackside at the Claude Robillard Centre. "Whether it comes or not, who knows?
"It's a great thing to aspire towards, but I'd love to win the race firstly, and run a personal best and if I manage to get the record that would be even sweeter."
Greene won the 400-metre hurdles at the 2010 Commonwealth Games in India and at the 2011 world championship in South Korea. He was captain of the British track team at the 2012 Olympics in London, where he finished fourth.
His last two seasons have been marred by injuries, but Greene hopes to be back fully fit this summer. Training for the 600 metres should improve his endurance for the hurdles.
It's his second attempt at the distance. In 2013 in Scotland, he ran 1:16.22, finishing second to American Duane Solomon (1:15.22).
What makes the 600 metres tricky is the seven entrants won't have their own lanes so jostling could be a problem.
"When you're not in your lane, there's the risk that people are going to bump into each other," he said. "I don't usually have that problem, being a 400 hurdler, but in this competition you have to be aware of the people around you all the time.
"If I have good pace from the start I'll have a chance to have a good time. Hopefully, there won't be too much argy-bargy (bumping)."
The field also has American Mark Wieczorek, Rafith Rodriguez of Colombia, Errol Nolan of Jamaica, Toronto's Philip Osei and Charles Philibert-Thiboutot of Quebec City.
"Some really world-class athletes have had a go at the record, so it's not an easy one," said Greene.
It will be the feature event of a weekend that has senior open events as well as national championships at the youth and junior levels.
"We wanted to add a special event that would bring some international class to the championship," said Laurent Godbout of the Quebec Athletics Federation. "There are some athletes who, during the wintertime, like to do these odd distance events like the 600."
The outdoor 600-metre record is much quicker: 1:12.81 by American Johnny Gray.
Another featured event is a likely hotly contested women's 800 metres, with Canadian Olympians Melissa Bishop of Eganville, Ont., and Jessica Smith of Vancouver as well as Karine Belleau-Beliveau of Montreal and Helen Crofts of Vancouver.