The Tigers need a run producer after Ordonez fractured his right ankle in Saturday's 3-2 loss to the Blue Jays, knocking him out for an estimated six to eight weeks.
If the Tigers were to acquire him, Dunn would be a designated hitter and play in the outfield. They already have a first baseman in Miguel Cabrera.
Nationals general manager Mike Rizzo has said in the past that he would want a lot in return if he were to trade Dunn. Tigers general manager Dave Dombrowski also indicated to local beat reporters that he would not trade top prospects for short-term players.
Dunn, who was hitting .279 with 23 home runs and 62 RBIs entering Sunday's action, is a free agent after the season.