Morse, 30, is available because the Nationals just re-signed first baseman Adam LaRoche to a two-year deal, sources said.
The Nationals have Bryce Harper, Jayson Werth and Denard Span in their starting outfield.
Several teams likely will be interested in the powerful Morse.
In 2012, Morse hit .291 with 18 homers and 62 RBIs. He had an OPS of .791. In 2011, he nailed 31 homers and had 95 RBIs in 146 games. His OPS was .910. He is not known for his glove work.
Morse would be a fit for the Yankees because he would add a right-handed bat to an outfield that features lefties Curtis Granderson, Brett Gardner and Ichiro Suzuki. Morse could also DH. The Yankees do not have a regular DH on their current roster.
Morse is due to make $6.75 million in 2013. He will be a free agent after the season.
The Yankees are still interested in free agent Scott Hairston. Hairston's agent, Casey Close, told ESPNNewYork.com on Monday that the Yankees and Mets are two of the contenders for his client.
A source with knowledge of the Yankees thinking told ESPNNewYork.com on Tuesday that the team is pessimistic, thinking that Hairston will prefer to sign with another club so he can get more at-bats. The Yankees have added Matt Diaz and Russ Canzler this winter as possible right-handed-hitting outfielders.