Artemis Racing member Simpson, nicknamed "Bart," died when the Swedish team's AC72 overturned while training on San Francisco Bay on Thursday.
The accident has plunged the Cup into uncertainty, fueling concerns over the safety of the 72-foot America's Cup catamarans and prompting Patrizio Bertelli, chief executive of the Prada fashion house and sponsor of Italian challenger Luna Rossa, to say he would consider pulling out his team.
America's Cup Regatta Director Iain Murray, spearheading the review of the incident, said Saturday that he has scheduled a meeting with all four teams --
defending champions Oracle of the United States, Artemis Racing, Emirates Team
New Zealand and Luna Rossa, for Tuesday in San Francisco.
"The meeting with the teams is a crucial next step," Murray said.
"We need to establish an open flow of information to ensure this review meets its goals of fact-finding and putting us in a position to recommend changes, if necessary."
The review will include study of all data that was captured at the time of the incident.
"Once we have the information, the basic facts, all the data, then we will be able to re-build the entire chain of events and start to assess why this incident resulted in a tragic loss of life," Murray said.
In the meantime, Artemis Racing on Saturday urged the sailing community to refrain from speculation.
"Until this process is complete, any conclusions being made about the events that led to the boat's capsizing and its tragic outcome are pure speculation," Artemis said in a statement posted on its website.
"Out of respect for Bart's memory and his family, we ask that the broader sailing community and others reserve judgment until all the facts are known, and not persist in unnecessary rumour."
But Simpson's death has cast a pall over the event.
Bertelli told Italian magazine Yacht Capital, in comments posted on the website yachtonline on Friday, that his team was taking the weekend to consider its position.
"The way it is now, it's not OK," Bertelli said.
"Those responsible must take note. Not everybody has understood that we're now in an extreme America's Cup, whereas it was romantic before."
"We're now like Formula One or rally," he said.
The excitement of those high-tech, high-speed motor-sports was just what billionaire Larry Ellison was going for when he pushed for the new parameters for the America's Cup craft.
Ellison's Oracle is the defending champion, defeating Switzerland's Alinghi in the 33rd edition in 2010 in a competition marred by legal wrangling over the rules that began after Alinghi won the 32nd renewal in 2007.
America's Cup chief executive Stephen Barclay said that in the wake of Simpson's death "nothing is off the table" as organizers consider their options.
But he voiced confidence that "the event in San Francisco will be a fantastic event."
He stressed that no decisions will be made until after the review into why the Artemis boat "nose-dived" and broke apart while turning.
Simpson, an Olympic champion sailor, was apparently trapped under a piece of the boat, and by the time he was found and pulled out of the water he could not be revived.
Prior to the tragedy, the 2013 America's Cup had already faced a number of legal challenges as well as questions about funding, environmental impact an participation.
Originally envisioned to include more than a dozen challengers battling for the right to take on Oracle in the final in September, the July 13-September 1 challenger series is now down to three -- the stricken Artemis, Luna Rossa and Emirates Team New Zealand.