The official announcement by Bradley, who lost the party's nomination to Al Gore in 2000, is likely to take place in Manchester on Tuesday morning at a previously unscheduled Dean event. Campaign sources will only say that "someone of Bradley's stature" will be there.
Campaigning in Iowa, Dean said he could neither confirm nor deny the report.
Bradley gave Gore a scare early in the 2000 primary process but eventually lost both the Iowa caucuses and the follow-up New Hampshire primary to the sitting vice president.
Bradley was a favorite of higher-educated, higher-income Democrats, according to party polls, a constituency that has leaned toward Dean in this year's contest.
The endorsement is further evidence of Dean's transformation from a political asterisk 12 months ago to the party's leading candidate. Dean secured Gore's endorsement last month and already leads in fund raising and in most state and national polls.
Bradley, 60, served three terms as senator from New Jersey, from 1979 to 1996. He was a Rhodes Scholar and an All-American basketball player at Princeton and later a star with the New York Knicks.