The two congressmen currently represent districts made up mostly of Detroit. Both were drastically redrawn by Republicans to add minority voters outside Detroit to make up for the city's shrinking population.
Democrats have said the new districts are examples of gerrymandering and are threatening to sue in federal court.
But Clarke spokeswoman Kim Bowman said Monday that Clarke had decided to switch districts rather than waiting. She says the 14th District includes more of the voters Clarke now represents.
Conyers' office is declining comment on whether the 82-year-old will swap districts with the 54-year-old Clarke.