Howard Wolfson, a top Clinton advisor, says the senator has personally asked some fellow top New York Democrats for their support in the event she goes ahead with such a campaign. "That process has begun," said Wolfson.
Wolfson says he doesn't know when Clinton may make a decision.
The former first lady is coming off an easy re-election victory to the New York Senate seat she has held since her historic election in 2000. National polls show her as the front-runner for the 2008 Democratic nomination.
Wolfson's comment marks a public acknowledgment of expections that once her re-election campaign was out of the way, Clinton would turn her attention to a possible White House bid.
Also eyeing the presidential race on the Democratic side, among others, are Senator Barack Obama of Illinois, former Senator John Edwards of North Carolina, Senator John Kerry of Massachusetts, Senator Evan Bayh of Indiana and Senator Joseph Biden of Delaware. Iowa Governor Tom Vilsack began his campaign for the nomination last week.
Clinton had been coy throughout the campaign but Wolfson made it clear Sunday that the planning is moving ahead. He said that, among other things, top Clinton aides have begun interviewing possible presidential campaign staffers in recent weeks.
Clinton already has a core of presidential campaign veterans on her staff and about $10 million left in the bank from her Senate campaign that can be converted to a presidential campaign. She also has her husband, former President Bill Clinton, as her main political adviser.
Wolfson said no decision had yet been made on when Clinton might formally create a presidential exploratory committee, a move that would allow her to begin legally raising money for a presidential campaign.
While Wolfson declined to say exactly which New York Democrats Clinton had been speaking to about her possible candidacy, The New York Times reported in its Sunday editions that she had already talked to Rep. Charles Rangel and state Democratic Chairman Herman Farrell about it.
While Rangel, who was instrumental in getting Clinton to run for Senate in 2000, told the Times the two had breakfast in New York City on Wednesday and discussed her plans, he would not provide details of their talk.
Farrell, a state assemblyman from Manhattan, told the Times he received a telephone call directly from her.
"I had a discussion with her about her decision to run for president. I'm not telling you what the decision was, only that we had the discussion," Farrell said.
"And I'm positive that if she runs, the people of the United States will elect her as our next president," Farrell added.
Pressure has been mounting on Clinton to send some sort of signal about her intentions since Obama let it be known that he might run. Wolfson said Sunday that was not a factor in Clinton's deliberations.