Willingham played in 114 games for Washington this past season and hit .268 with 16 home runs and 56 RBIs. He missed the final month and a half of the season because of a torn meniscus in his left knee.
Willingham said recently that the knee is getting better, and he will start swinging a bat and throwing a baseball around Christmas time.
"The Nationals have a right to do whatever they want," Sosnick said via phone. "It's part of the arbitration process. They are in no obligation to offer him a multiyear deal. He is under control for one more year."
But a baseball source familiar with the Nationals' thinking believes Willingham will most likely be traded before the 2011 season starts. The source believes that Washington would want something for Willingham before he becomes a free agent after the 2011 season. Published reports already indicated that several teams have interest in Willingham's services.
Sosnick declined to comment on the possibility of Willingham being traded and general manager Mike Rizzo wasn't available to comment.