A Rasmussen poll released Friday gave Manchin 51 percent of the vote in a hypothetical match-up with Raese, who had 35 percent of voters' support.
Manchin has the support of 78 percent of Democrats, according to the survey of 500 likely voters.
State Democratic Party Chairman Larry Puccio, a former Manchin aide and the governor's longtime confidante, said his party has "three great candidates that will work extremely hard to secure the vote of the Democrats."
Despite his close ties to Manchin, Puccio said he will remain neutral in the primary.
"I have been a longtime friend of the governor, and I've been a friend of Ken Hechler," said Puccio, who became party chairman last month. "I know Sheirl Fletcher . . . They're good Democrats and they work very, very hard."
Former Manchin general counsel Carte Goodwin was appointed by Manchin last week to fill the Senate seat until the election.
Secretary of State Natalie Tennant will certify the candidates Saturday, when she also will hold a random drawing to determine what order candidates' names appear on the primary ballots.
Reach Alison Knezevich at alis...@wvgazette.com or 304-348-1240.