Cohen, a non-practicing Jew, announced he would run for the office of Labor Party chairman after its current leader, Wouter Bos, said he would resign the post.
Dutch news agencies reported that Cohen had over 50% of votes, giving him a substantial advantage over his two opponents, Christian Democrat leader and outgoing Prime Minister Jan Peter Balkenende, and far-right PVV leader Geert Wilders.
A poll conducted by Maurice de Hond gives Cohen 55% of votes, Balkenende 25%, and Wilders 17%.
Another poll of 16,000 people by TV show EenVandaag showed 52% of voters would prefer Cohen as prime minister, compared with 17 and 15 percent for Balkenende and Wilders respectively.
Wouter Bos submitted his resignation over controversy regarding placement of Dutch forces in Afghanistan. He said he was leaving politics to devote more time to his family.
The two polls show percentage of backing for the three candidates, not support for their parties, but a win for Cohen is expected to rake in more votes for the floundering Labor Party and shift public backing from Wilders' far-right party.
Cohen, who is known for his inter-culture politics, helped relieve tensions in Amsterdam in 2004 after the assassination of anti-Muslim filmmaker Theo Van-Gogh. The mayor met with Muslim leaders and succeeded in preventing rioting following the death.
Reuters contributed to this report