JACKSON (AP) — Even in explaining his decision to not to seek re-election in 2008, Republican U.S. Rep. Chip Pickering said publicly for the first time Friday that he might have his eye on the Governor’s Mansion.

‘‘Maybe,’’ Pickering said, responding to a question about whether he might run for the top job in state government — a move that would be at least four years away.

And, there was this response to a question about the longtime speculation that he might want to run for U.S. Senate: ‘‘As my oldest son would say, ‘when the bridge crosses the river, we’ll get to it.’’’

Pickering, 44, announced in a news release Thursday that he won’t seek a seventh, two-year term in 2008 because he wants to spend more time with his wife, Leisha, and their five sons, who range in age from 8 to 17.

Surrounded by relatives, staff members and supporters during a news conference Friday at the Mississippi Republican headquarters, Pickering said he’s not planning to leave politics forever. But after being in public service for 18 years — 11 in Congress, four as a staff member for Republican Sen. Trent Lott and three in the Agriculture Department under the first President Bush — Pickering said it’s time for a change.

‘‘If I am ever going to broaden my experience in life, to enter the private arena and hopefully get experiences that will not only make me a better person but one day could help make me a better leader, this is the time that I think is best for me to do so,’’ Pickering said as Leisha stood by his side and fought tears.

Pickering makes $165,200 a year in Congress. He said he does not have a new job lined up. In 2003, he turned down a $1 million-dollar-a-year lobbying job as president of the Washington-based Cellular Telecommunications and Internet Association.

Mississippi’s next U.S. Senate race is in 2008, when Republican Thad Cochran is up. Although he hasn’t announced his plans, Cochran has been raising money for re-election. Pickering’s mentor, Lott, is up again in 2012.

For Pickering’s first decade in Congress, Republicans were in the majority. That changed after last November’s elections, and he said the change played ‘‘some part’’ in his decision not to run again.

‘‘It is different being in the minority. And for my temperament and personality, probably being in the majority and building the coalitions to govern is — I’m more suited for that,’’ Pickering said.

He also said that since Democrats took over, member of Congress have been required to spend more time in Washington. He said the House used to vote on legislation on Tuesdays, Wednesdays and Thursdays, but since January, the schedule has often included Mondays on Capitol Hill.

Pickering said he has been coaching his sons’ fifth and sixth grade football teams at Jackson Academy the past four years, and those teams play their games on Monday nights.

His decision not to run again creates a free-for-all contest for a rare, open congressional seat in Mississippi.

‘‘It’s going to be a donnybrook,’’ said Jackson businessman Billy Mounger, a longtime financial supporter of Pickering and many other prominent Republican politicians.

Pickering was first elected in 1996. His district makes a diagonal across the state, from the southwestern corner up through the Jackson metro area and to Noxubee County.

Potential candidates are already lining up. But, Republican Lieutenant Governor Amy Tuck, who might have been a front-runner, said Friday that she is not running.

Candidates’ qualifying dates will be Jan. 1-11. The party primaries will be March 11.

Among those who say they’re thinking of running:

— Republican state Sen. Charlie Ross, who was defeated in the Aug. 7 GOP primary for lieutenant governor.

— Gregg Harper, an attorney who has served as Rankin County Republican chairman.

— Joe Nosef, who had worked as a staff attorney for Republican Gov. Haley Barbour and is now Barbour’s campaign manager. ‘‘But I have to tell you that right now all I am focused on is getting the Governor re-elected,’’ Nosef said.

— Heath Hall, who worked as spokesman for Republican Gov. Kirk Fordice during the 1990s and is now vice president of the Mississippi Technology Alliance.

— Nick Walters, who worked from 2001-06 as state director of the U.S. Department of Agriculture’s Office of Rural Development.

While Pickering appeared at ease during the news conference Friday, a small verbal slip revealed a bit of nervousness.

‘‘As I dropped my son off this morning at school, I gave him some advice. He is in the ninth grade. He is playing in a junior high jamboree tonight as quarterback. I said the key to your success is being compoised — uh — composed,’’ Pickering said.

A wave a laughter filled the room.

‘‘Poised,’’ he said. ‘‘And to be cool under fire.’’