The 2015-16 Louis Vuitton America's Cup World Series, which concludes in Fukuoka this month, is being contested by teams from Britain, New Zealand, Japan, Sweden, France and the US.
Those six syndicates will take part in two qualifying competitions next May and June, with the winner to take on defending champion Oracle Team USA in the main event in Bermuda.
"It will be a goal for anyone involved in the America's Cup in the future to have more competitive teams involved," Coutts, the chief executive officer of the America's Cup Event Authority, told CNN by phone from New Zealand.
Expansion to "10 or 12 teams" is "definitely a goal for the future," he added.
'F1 on water'
The America's Cup is the oldest trophy in international sports, dating back to 1851.
It had a major revamp in 2013, aimed at turning the elite sailing series into "Formula One on water," complete with high-tech 72-foot catamarans capable of going as fast as 50 miles per hour (80.47 kph) and virtual on-screen graphics explaining proceedings to television audiences.
"We are getting a lot of interest from teams wanting to join in for the future," Coutts said. "We don't have the racing (like) in the past, with one of two teams that were dominating. And that's drawing more viewers in."
He also pointed out that all World Series teams bar one have hosted races in their own respective countries, increasing the event's exposure.
The 54-year-old Coutts is one of New Zealand's most famous sailors.
He clinched Olympic gold in the Finn Class at the 1984 Los Angeles Olympics and won the America's Cup in 1995 and 2000 as skipper of Team New Zealand, and then in 2003 with Swiss challenger Alinghi.
He was also chief executive officer of the winning 2010 and 2013 teams, bankrolled by Oracle software billionaire Larry Ellison.
Teams are usually funded by rich benefactors, major corporate sponsors and government contributions.
The British syndicate headed by Olympic sailing legend Ben Ainslie, which leads the World Series standings ahead of the November 18-20 finale in Fukuoka
, is backed by car manufacturer Land Rover but received £6.5 million from the UK government
to build its Portsmouth base.
It also has the Duchess of Cambridge, Kate Middleton, as royal patron of its 1851 trust.
Although the 2013 America's Cup in San Francisco was a success for broadcasters and even won an Emmy Award, the $100 million price tags for the boats meant there were only three challengers.
In an attempt to attract more competitors, organizers decided last year that the 35th edition of the America's Cup in Bermuda would be held in much smaller and cheaper boats.
"Right now, with the cost-cutting measures that have happened, that's really making it much more attractive," Coutts said.
"And also the increased media appeal, which is drawing more partners to the America's Cup, that's appealing to potential new teams."