School board member Robert Scales introduced the idea and is asking the board to form a committee to study the proposal.
The proposal would change the name of Conover Road Primary School, which serves students from pre-kindergarten through second grade.
The proposal to name the school after Trump has drawn mixed reactions from residents.
Mohammad Chater said, "I mean, I think he really hasn't done anything of monumental importance for a school to be named after him."
While Sonja Gregoire disagreed, saying, "I think it's great. It's all positive. Trump has really done a lot for our country. I'm 100% for it."
Joe Reinbold said, "I don't think that things should be named for a sitting president. I mean, it's all right to memorialize them after a while, but it seems like Trump wants everything in this area named for him."