SACRAMENTO, Calif. — With Arnold Schwarzenegger’s governorship entering its final years and his ability to attract the spotlight intact, one question is arising more frequently: What will Arnold do?

Will he share the stage with Al Gore as a global environmental crusader, promote green technology for a Barack Obama administration, run for the U.S. Senate? Or might he pursue political reform on a broader scale, as he has hinted in appearances with New York City Mayor Michael Bloomberg, who shares Schwarzenegger’s independent streak?

Any of the options that would give him a larger platform undoubtedly would be more appealing than dealing with the gridlock inside California’s Capitol.

The partisan finger-wagging has kept him wrapped up in negotiations over faltering state finances for much of the last two years, and his approval ratings have followed the decline in California’s economic fortunes.

The 61-year-old Republican governor has been asked repeatedly whether he would entertain a position if offered one by the Democratic president-elect, most likely focused on alternative energy or other environmental initiatives.

He’s been coy in some of his answers, but has said he will remain in office until the end of his term in January 2011. He is not eligible to run again for governor.

Schwarzenegger enjoyed a brief diversion from the budget frustrations as he mingled recently with leaders from 19 countries at the global warming summit organized by his administration.

Schwarzenegger has successfully branded himself as a modern environmental activist by repeating the same message: Cut emissions and invest in green technologies such as solar and wind power.

That image has held even though implementation of Schwarzenegger’s signature policy — the 2006 law seeking to cut emissions roughly a third by 2020 — is so complex that it won’t be completed until after he leaves office.

Schwarzenegger’s name comes up as a possible U.S. Senate candidate should Sen. Dianne Feinstein decide to run for governor in 2010 or if he chose to run against Sen. Barbara Boxer. Both are Democrats.

One of the biggest wild cards is the governor’s wife, Maria Shriver. A Democrat and early supporter of Obama, she was caught off guard in 2003 when Schwarzenegger announced his intention to run in the recall election for governor.

Schwarzenegger says that won’t happen next time.

“Before I make any move, the next move that I make, I’m going to go and say to Maria: ‘Maria, you tell me what to do,”’ Schwarzenegger said in a recent Fox News interview.

A reprise of his Hollywood career seems unlikely. The film star who earned $30 million in his final “Terminator” movie now says he’d rather be an action hero on weightier matters such as alternative energy and rebuilding the nation’s infrastructure.