At Dallas, Davids, 33, would join a team whose biggest name is Guatemalen goalkeeper Carlos Ruiz.
Davids' career includes spells in several European leagues, having played for Dutch club Ajax, Juventus in Italy and Barcelona in Spain.
The MLS was propelled into global headlines this week when former England captain Beckham signed with the Los Angeles Galaxy, inking a five-year contract that industry analysts say is worth some $250 million to the player.
An influx of foreign talent was made possible in November when the league approved a new rule allowing teams to go above the two million-dollar per team salary cap to acquire a "designated player".
Each team will receive one "designated player" spot on its roster, and while they can be traded among teams no team will be able to have more than two such players.