In an interview with The Associated Press, McGinn said he thought $15 was a "fair starting point."
He cautioned that the process was best handled legislatively and that the actual number would be determined by city councilmembers. He says he would support the council if it wanted to set a minimum wage above $15.
McGinn is up for re-election next month. He says if voters choose to keep him for another four years, he plans to put together a coalition to "figure out how far we could go on the minimum wage."
McGinn challenger Ed Murray has said he would push for a $15 minimum wage but planned to proceed with a phased-in approach.
Washington already has the nation's highest state minimum wage at $9.19 an hour.