PHOENIX — Is Rep. Gabrielle Giffords running for re-election?

That’s a question State Sen. Frank Antenori of Tucson wants to answer before the May 15 deadline for submitting nominating petitions. The first potential candidate to publicly declare an interest in running for the southern Arizona post, Antenori said Thursday he feels Democrats are exploiting a perception that she’s running for re-election as a way to blunt attempts by the GOP to win the seat.

“You are not going to use this strategy for a political purpose and try to keep Republicans out of the race until May. Ain’t gonna happen,” Antenori said, explaining that such a late announcement by Giffords would leave GOP candidates flat-footed.

Giffords, who is in her third term in Congress but has spent the past eight months recovering from a gunshot wound she suffered during a meeting with voters, hasn’t publicly said whether she’ll seek re-election. She also has been mentioned as a potential candidate for a U.S. Senate seat next year.

Arizona Democratic Party spokeswoman Jennifer Johnson said the decision on whether Giffords will run is for the congresswoman and her family to make. “Her recovery isn’t based on (Antenori’s) political ambitions,” Johnson said.

Speculation on Giffords’ future has buzzed since her surprise return to Congress earlier this month to cast her first vote since the Jan. 8 shooting in Tucson that wounded 12 others and killed six people, including one of her aides. Her return to vote on the debt ceiling deal was celebrated as proof she could possibly return full-time to politics.

Giffords campaign chairman Michael McNulty didn’t immediately return calls placed Thursday.

Some Republicans have privately expressed reluctance in speaking publicly about the future of the seat because of sensitivities of commenting on her career as she was recovering.

Antenori, who formed an exploratory committee for a potential congressional run, said three weeks ago he thought Giffords was going to run, but now is left to wonder after a loyal Giffords aide took another job and, he charges, the Democratic Party is testing the waters for other possible candidates for the post.

“If she is capable and has the physical ability to represent the district, I think she would be a formidable — almost unbeatable — foe,” Antenori said. He’s the only candidate so far who has said publicly he’s even considering a run — but he also says he will probably cancel those plans if Giffords decides to make another bid for her seat.

Johnson said the party isn’t shopping around possible candidates for the post. “Congresswoman Giffords is our incumbent,” Johnson said. “If she decides not to run, then that’s the only appropriate time for us to be discussing other Democratic candidates.”

Antenori said he plans to announce whether he’s running in January or February after the state finishes drawing new boundaries for the congressional district. He believes Giffords ought to make her announcement within the first two months of 2012, too.

Antenori, who served in the Army in Afghanistan and Iraq before retiring from the military in 2004, lost a 2006 run for the congressional post, finishing second to last in a primary field of five Republicans. He went on to win a 2008 state House race and crushed his Democratic opponent in a 2010 race for the state Senate.

If Giffords decides to run again, she will have plenty of goodwill and money at her disposal. Democratic colleagues have held several fundraisers on her behalf in recent months and many are also donating to her campaign. As of June 30, they had helped her campaign generate more than $639,000 in donations.

According to the latest quarterly report filed with the Federal Election Commission, Giffords’ campaign has nearly $788,000 in the bank.

Bruce Merrill, a longtime pollster in Arizona and senior research fellow at Arizona State University’s Morrison Institute for Public Policy, said Antenori is trying to put his name out to voters in case Giffords decides against running for re-election. “People should, rightfully, try to position themselves,” Merrill said.

But Merrill, who believes the Democrat is unbeatable if she seeks re-election, also speculated that Giffords probably wants as much time as possible to assess her health and whether she wants to run again.

“There is no reason, in my opinion, for her to announce until May,” Merrill said.