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“This is not only a matter of fairness, but would also help the federal government attract, recruit and retain the most qualified workers, at a time when the number of federal employees eligible to retire is steadily increasing,” said Sen. Joe Lieberman, Connecticut independent and a bill sponsor.

Mr. Obama is considering nominating Mr. White for deputy chief management officer for the Pentagon — a Senate-confirmed position created last year by Congress to help with management of the sprawling Defense Department.

If confirmed, he likely would face questions during a Senate confirmation hearing over how his nomination would square with the military’s policies on gays — though as a civilian position, he would not run afoul of the policy.

In 1993, President Clinton signed into law “don’t ask, don’t tell” in which openly gay service members have been expelled from the military.

The Palm Center, the think tank where Mr. Frank is a fellow, said Mr. Obama could use national security grounds to halt expulsions under the law.

Mr. Frank said nominating an openly gay person wouldn’t signal how Mr. Obama plans to proceed on the ban on gay servicemembers.

Neither the Defense Department nor the White House would comment on Mr. White’s potential nomination, and Mr. White’s spokeswoman said he couldn’t be reached for comment.

Last year, The Times reported that Mr. White was being backed by top retired military officials to be Navy secretary, though that position went to Ray Mabus.

As head of the Intrepid, a museum based on the retired aircraft carrier of the same name, Mr. White has been widely praised by military officials and politicians, and appears to have a strong network of supporters backing him for a government office.