Duterte, 76, is barred by the constitution from seeking a second term as president, but he last week gave the strongest signal yet that he might run for vice president.
The posts are elected separately.
The survey of 2,400 respondents by Pulse Asia, held between June 7 and 16, put Duterte top among 15 potential candidates for vice president, with 18 per cent of the vote, and ranked daughter Sara number one in the presidential contest, with 28 per cent support.
Duterte's critics believe he could be making a play for retaining power through the number two post, by taking over as president from an ally who wins, then resigns the presidency.
Duterte's legal counsel Salvador Panelo has dismissed that idea as "farfetched".
It was the first time Pulse Asia included the Philippine leader as a potential contender for the May 2022 elections.
The survey was conducted before Duterte had said he was seriously considering the vice presidency.
Daughter Sara, who succeeded him as Davao mayor, was top of the poll for the third successive time, ahead of 14 others, including boxing icon and politician Manny Pacquiao.
Last week, Duterte-Carpio, 42, was quoted in media as saying she was open to running for president, months after telling Reuters she had no interest in the job.
The president on Monday (July 12) reiterated he did not want Sara to run to spare her "from the vagaries of politics in the Philippines".