The North Carolina senator had 72 percent support as a vice presidential candidate in a CNN/USA Today/Gallup poll published Wednesday.
Rep. Dick Gephardt of Missouri was second with 64 percent support.
While Kerry has said little about his consideration of a running mate so far, the four-day Democratic National Convention begins July 26 in Boston, and Kerry is expected to accept the presidential nomination.
Edwards was Kerry's strongest rival during the primaries and has campaigned for Kerry in recent weeks. The two men had a private meeting last week on Capitol Hill.
Their percentage ratings were rated at 59, 58 and 54, respectively.
The poll was based on interviews with 1,005 adult U.S. citizens contacted by telephone Monday through Wednesday.