Some members of the Nationals believe that Winn, 36, will accept a role off the bench. Washington had interest in Winn last year before he reached a deal with the Yankees.
This past season, Winn spent a portion of his time on the bench. He played in a combined 116 games for the Yankees and Cardinals and hit .239 with four home runs and 24 RBIs.
The Nationals most likely will not seek bench help until after the Winter Meetings come to an end.