PHOENIX — Eight months before the primary, state Treasurer Doug Ducey already has raised more private cash in his bid for governor than his publicly funded foes have any chance of getting.

In a press release Monday, Ducey announced he has raised $1.05 million since forming an exploratory bid for governor last July, and after expenses, has $923,000 in the bank.

That already gives him a leg up on Secretary of State Ken Bennett, who is in the race but will seek public financing for his campaign, which means the most he can get is $753,616, since the U.S. Supreme Court wiped out provisions of the voter-approved law giving a dollar-for-dollar increase over that amount when privately funded foes spent more.

Ditto for other Republicans who have said they intend to rely on public funding, including state Sen. Al Melvin and former Maricopa County Attorney Andrew Thomas.

But Ducey may have another motive in issuing a press release more than three weeks before his campaign finance report is due to be filed: Keep the GOP field from getting any larger.

Mesa Mayor Scott Smith has promised a decision about a gubernatorial run this month.

Smith did not return calls for comment, and an aide to Ducey said he was “unavailable’’ Monday to speak to the media.

But Melissa DeLaney, his press aide, insisted Ducey’s decision to issue a press release weeks ahead of actually filing the legally required disclosure — including a list of contributors — was because “we have a lot of supporters we wanted to show our gratitude to.’’

In a prepared statement, Ducey hinted he could easily raise a lot more.

He pointed out most of his donations came under the old limits of $912 per donor. But the Arizona Supreme Court recently upheld legislation boosting the limit to $4,000, with Ducey’s statement saying that creates “substantial room for further fundraising.’’

Christine Jones, former legal counsel for Web hosting company GoDaddy, also is in the mix.

The winner of the Republican primary will face off against likely Democrat contender Fred DuVal, also running with private dollars. Others in that race include perennial Libertarian hopeful Barry Hess and independent radio station owner Rick Murphy of Lake Havasu City.