WASHINGTON (REUTERS) - Michele Flournoy, a former top US Department of Defence official widely tipped as a possible replacement for Defence Secretary Chuck Hagel, has taken herself out of consideration for the job, according to multiple sources familiar with the circumstances.

Flournoy, co-founder and chief executive of the Centre for a New American Security wrote to the think tank's board of directors saying she would remain in her post and had asked President Barack Obama to remove her from consideration to head the Pentagon, the sources told Reuters on Tuesday.

One of the sources said Flournoy, whose youngest child is 13, had cited family reasons for her decision.

Flournoy would have been the first woman to head the Defence Department if she had been nominated and confirmed in the post. Her decision to drop out of the running was first reported earlier on Tuesday by Foreign Policy magazine.

Hagel announced his resignation on Monday.

Flournoy's decision leaves Ashton Carter, former deputy defence secretary, and the current deputy, Robert Work, as the top potential candidates for the job. Spokesmen for both Carter and Work declined to comment.

Foreign Policy said the White House could also look to Representative Adam Smith, the top Democrat on the House Armed Services Committee, to fill the post.

Smith's office declined comment.

Obama is not expected to announce his choice this week.

"The president is considering a number of well qualified candidates, however, I don't have any personnel announcements at this time," said a senior admininstration official.