His announcement is tentatively set for 10 a.m. EST at Stamford High School, an aide said, followed by one of his trademark visits to a local diner.
Leading Connecticut Democrats say Lieberman told them this past Monday at a 90-minute meeting in New Haven that he plans to run. Several said they were almost certain he will run, based on his recent actions and comments.
But Senate Democratic leader Tom Daschle offered a reminder this week that talking about running is not the same as formally announcing a decision.
The South Dakota Democrat said Tuesday he will not run, after saying as recently as Sunday night that he was leaning toward a run. Daschle aides had already set an event to announce his candidacy and were planning trips to states with early contests.
Connecticut Democrats said Lieberman, during the meeting at a New Haven hotel, talked about the importance of his ties to Connecticut and shared with his audience some factors he has had to consider.
"The discussions were about the process, the decision, the challenges," said John Olsen, head of the state AFL-CIO.
"All of us in that room felt that Joe Lieberman offers a tremendous amount of character and leadership to America," said New Haven Mayor John DeStefano. Those who attended the Monday meeting will be very surprised if Lieberman doesn't run, he said.
Lieberman aides would not confirm accounts of the New Haven meeting.
"This is the senator's decision to announce," Lieberman spokesman Dan Gerstein said Wednesday.
Fellow Sens. John Kerry of Massachusetts and John Edwards of North Carolina are seeking the Democratic nomination. Sens. Bob Graham of Florida and Joseph Biden of Delaware are also considering a White House bid. Vermont Gov. Howard Dean and Rep. Dick Gephardt of Missouri are also in the race, and Gen. Wesley Clark of Arkansas is considering a run.
Al Gore, the 2000 Democratic nominee, probably would have dominated the field if he had run. But he said in mid-December that he was not entering the race. That decision freed Lieberman to consider a run, because he had pledged not to oppose his running mate in the last presidential election.
By Will Lester