"It is Sara-Go," Mr Duterte said in response.
When asked to confirm what the president said, Ms Duterte-Carpio's spokesperson, Mayor Christina Garcia Frasco told Reuters: "The extent of my knowledge is also what was reported in local news. We have no comment on the same."
ABS-CBN News said it obtained permission from the broadcast journalist to use the video showing Duterte outside a hotel in Manila where the registration of candidates was taking place, and that a transcript was also provided.
In the same clip, Mr Duterte was asked when his daughter would file her candidacy for president, he said: "I really do not know. I do not have any idea at all".
Asked if he had given his daughter permission to run for president, he said: "Ah, no, actually we don't talk about politics, ever since we never talk about politics. I would say that it is for the better," Mr Duterte was quoted as saying.
Mr Duterte, 76, said on Saturday he was retiring from politics, a surprise move that fuelled speculation he was clearing the way for a presidential run by his daughter.
He had been expected to run for the No. 2 job, a plan most Filipinos oppose as violating the spirit of the constitution which sets a one-term limit for the president to stop power being abused.
Ms Duterte-Carpio's mayoral re-election filing, did little to douse speculation she has her eye on the presidency.
Political analysts were sceptical, noting that last-minute changes were still possible, as in 2015 when Mr Duterte entered the presidential election race at the eleventh hour and won by a huge margin, and Ms Duterte-Carpio, they said, could do the same.
Candidates have until 8 October to register, but withdrawals and substitutions are allowed until 15 November, leaving scope for last-minute changes of heart.