Two Florida-based "household name" companies have met multiple times with a private booster group to discuss a naming rights deal for a new Tampa Bay Rays stadium, said one of the leaders of that group.

Tampa lawyer Ron Christaldi, co-founder of Rays 2020, declined to name the companies, but said the multi-year deal for the proposed Ybor City ballpark could be in the range of $5 to $10 million a year.

That figure falls within the range of what national experts have predicted for the Rays.

Rays president Matt Silverman issued a statement about the talks on Monday.

"From all accounts, they are working diligently on corporate support and we are very grateful," Silverman said.

Christaldi framed the naming rights discussions as part of a gathering corporate momentum in support of bringing Major League Baseball to Florida's third-largest city. Earlier this month, he said his group had received pledges of $160 million in new support — think suites and sponsorships — over a ten-year period.

Rays 2020, formed in part to solicit corporate backing for the stadium, has contacted about 40 percent of approximately 400 targeted companies, he said Friday.

Many companies that initially held back on ponying up cash toward the proposed stadium just north of Adamo Drive are starting to show more interest, he said, again declining to name specific companies or amounts.

Meanwhile, pressure is mounting as the clock ticks on a Dec. 31 deadline for the team to explore stadium sites around Tampa Bay as was agreed to by the Rays and St. Petersburg, where the team has played since its 1998 inaugural season.

Once a more clear financing picture emerges by the end of the year, Christaldi said he expects more corporate money to surface.

"They just want a little more, they just don't have all the details yet," he said.

Naming rights deals often are used by teams to help finance new ballparks.

The Texas Rangers, who will play in a new Arlington stadium in 2020, extended their deal last year with Oklahoma City-based insurer Globe Life through 2048 at the hefty price tag of $11 million a year. The Atlanta Braves signed up Sun Trust Bank in a 25-year deal said to be worth more than $10 million a year for their new digs in suburban Cobb County.

The Rays' current naming rights deal at Tropicana Field with the Bradenton orange-juice maker is reportedly one of the cheapest in Major League Baseball.

Typically, naming rights revenues stay with the team instead of being shared with local governments. The guarantee of annual cash flow can be used to borrow money for construction of a new ballpark, which could cost upward of $800 million. A long-term, $10 million-a-year deal could raise about $95 million up front, sports economists have said.

Contact Charlie Frago at cfrago@tampabay.com. Follow@CharlieFrago