The sources, who spoke on the condition of anonymity, said Democrats urged Mrs. Gore to run after Sen. Fred Thompson, R-Tenn., announced last Friday that he would not seek re-election.
One of the sources said Mrs. Gore was committed to public service and believed she owed it to herself to give some thought to a run.
Her husband, Al Gore, held the Senate seat from 1985 to 1993, before becoming vice president. Gore said he would not run for his old seat immediately after Thompson made his announcement.
One Democratic operative close to the Gores, speaking on condition of anonymity, said Mrs. Gore had received a handful of overtures from Democrats urging her to consider running for the Senate and Mrs. Gore was weighing them.
However, the official said that it does not appear likely that Mrs. Gore would run, given her tendency to shrink from the limelight during the presidential campaign and her general unease about the national political process. Still, the official, said it was telling that Mrs. Gore did not reject the overtures out of hand.
A Democratic official who spoke with Al Gore on Thursday said the former vice president said his wife was talking to people in Tennessee who are eager for her to run and is thinking through the possibility of a Senate campaign.
Jano Cabrera, a spokesman for the couple, said Mrs. Gore was in Los Angeles Thursday and could not immediately be reached.
Earlier, Cabrera said the Gores are house hunting in Nashville.
Gore has been dividing his time between Washington and Tennessee, where he is teaching at two universities in the Nashville area.
Cabrera said the Gores will keep their farm near Carthage, where Gore's mother lives, as well as a house in Arlington, Va., that has been in Tipper Gore's family for 60 years.
Gore says he has not decided whether he will run for president again, but he recently formed a leadership political action committee that he says will support Democratic candidates nationwide.