The matchups for the fourth round, to be played in June, are based geographically, and lower-division teams must meet stadium criteria to host MLS clubs.
The Fire could play at the Premier Development League giants Michigan Bucks if the fourth-tier team gets past USL club Saint Louis FC in the third round. The Bucks beat the NASL's Indy Eleven in Wednesday's second round.
There are three games featuring a pair of MLS teams, as the Seattle Sounders host the rival Portland Timbers, New York City FC goes across the river to play at the Red Bulls, and Minnesota United travels to Sporting Kansas City.
The only question of opponents involved the MLS clubs from Texas, with the Houston Dynamo drawn against the winner of the NASL's North Carolina FC and the USL's Charlotte Independence.