Mr Duterte’s spokesman Harry Roque said the president had a “real, genuine wish to step down” if a qualified leader like Ferdinand Marcos Jr was in place to take the top job.
The president won power in 2016 and his term in office doesn’t end until June 2022, but he has spoken repeatedly about leaving office early. He said at two separate events on Tuesday that he was “ready to go”.
The president is believed to be reluctant to leave immediately, however, because it would mean handing power to Vice President Leni Robredo, whom he said is not up to the job.
Ms Robredo, who leads the opposition Liberal Party, was elected vice president in a separate election in 2016, having narrowly defeated Mr Marcos Jr.
Yet the son of the ousted former ruler challenged the result by alleging fraud, prompting the Supreme Court to order a recount. The legal process got underway in April this year but could still take several years to resolve.
“If there’s development and (Mr Marcos Jr) will win the protest and he becomes the vice president, yes, (Mr Duterte) will make true his word,” said Mr Roque at a press briefing on Thursday.
Mr Marcos Jr, who represents the political party founded by his father, responded by thanking Mr Duterte for his support. But he also encouraged the president to finish his term.
“I urge him not to leave the presidency as our people still need him for the betterment of our lives and our country,” he said in a statement.
Mr Marcos Jr, better known as “Bongbong”, is one of the notorious former dictator’s three children. Ferdinand Marcos ruled the Philippines between 1965 and 1986, before he and his family were forced into exile in Hawaii.
Bongbong’s official Instagram account contains several photos of him alongside his father.
Educated at Oxford University, Bongbong returned to the Philippines in 1992 to become a congressman for the Ilocos Norte province.
Although he avoids discussing his father’s rule, Mr Marcos Jr has talked about his pride in the family name.
“I have only felt it to be an advantage, a blessing. I am very thankful that I am a Marcos.”
Additional reporting by agencies