Gerard Collomb's announcement follows the abrupt resignations in recent weeks of Macron's popular environment minister who criticized Macron's commitment to climate change green issues and his sports minister, Reuters reported.
Collomb, who recently acknowledged what he called a "lack of humility" Macron's administration, suggested that he could stand down as soon as the middle of next year.
"I won't be interior minister up to the last minute," he told the magazine in an interview.
"Ministers who want to run in the 2020 municipal elections should in my view leave the government after the European (parliament) elections," he said.
The European vote takes place in May 2019.
He was among the first heavyweight Socialist Party members to defect and join the political movement Macron formed when he launched his run for president.
Collomb served as Lyon mayor from 2001 to 2017, quitting the post to join 40-year-old Macron's government after he won power in May 2017.