However, he said was reluctant to do that now because a constitutional succession would mean handing power to Vice President Leni Robredo, whom he said was not up to the job.
Marcos, better known as “Bongbong”, has challenged the result alleging fraud.
The Supreme Court has ordered a recount, a complex process that got underway in April and could take several years.
Robredo says she won fairly.
Duterte’s spokesman, Harry Roque, said the president had a “real, genuine wish to step down” if a qualified leader could replace him. Marcos was among those he would prefer, Roque said.
“If there’s development and he will win the protest and he becomes the vice president, yes, he will make true his word,” Roque told a regular news briefing.
In a statement, Marcos expressed his gratitude to Duterte for showing faith in him, but said the president should 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,” Marcos said.