Friday, team president Brian Auld asked for open minds in order for the team to remain in Tampa Bay beyond 2027.
He spoke at a weekly forum called Cafe Con Tampa, hosted by PR agency Tucker Hall.
"The tricky thing is trying to balance the magic of a postseason run with the urgency and importance around our situation," Auld said. "This is why we are asking everyone to keep an open mind."
Auld said the Tampa Ybor stadium plan fizzled because there wasn't enough public funding, demand for season tickets, or corporate support.
But he says a Tampa Bay-Montreal split season would maximize comfortable weather, allow for cheaper stadiums, and bring in two TV deals.
"The vast majority of our fans go to between one and three games each year," he said. "If we can get those fans to go to the same number of games at a new, outdoor, state-of-the-art facility, and do the same thing in Montreal, we will have doubled our attendance."
He did not say how negotiations are going in St Pete, but the city spokesperson Ben Kirby said, "In order to continue the constructive dialogue, the mayor has no comments in reaction to Mr. Auld's remarks."
This week, owner Stu Sternberg apologized publicly for a plan to advertise the split city idea at Tropicana Field during the upcoming playoffs.
"I would like them to be here full time, but I am very much open to listening to their proposals for a split season," said St. Pete City Council Chair Ed Montanari.
Auld said attendance is falling short by over 50%, which gives the team a case to make for squeezing the entire season into 40 games in both areas, pushing up overall attendance.
"When you ask the hard questions, we have concluded it is next to impossible that full-season baseball can succeed in Tampa Bay today," said Auld.
He finished with this reminder: "There are still great seats available for the American League Division Series."
Auld said the Rays have not always done a perfect job of making their public case for a new stadium.
These plans would have to be approved by both local governments, Major League Baseball, and the players' union.