Stewart, who was sworn in this week, has previously served as executive director of The Hope Center, a shelter for homeless women.
Evans said the county, which oversees health and human services, needs to participate with the city in the homeless day center.
“I think that is something that we need to address,” he said.
Evans, who was homeless himself in the 1980s, said he could see the benefit of a homeless day center where people can be referred to social services.
“I was homeless in Washington, D.C., and I did not have a clue as to where to go to find the information that I needed to be a productive member of that community," he said.