"Why not? The Nationals have a good team, but I have something to finish in Chicago," he said. "I love Chicago. If the Cubs can get a piece that can make them better, that's all I want.
"I heard from our reporters. The Nationals are looking for a center fielder and my name was in the mix. Like I said, it's always something. Rumors are out there. It will be interesting."
Byrd played for the Nationals in 2005 and 2006, and hit a combined .245 with seven home runs and 44 RBIs. Since then, however, Byrd was able to find his swing with the Rangers and Cubs, and credits Cubs hitting coach Rudy Jaramillo for his success.
If Byrd is not traded, he can become a free agent after the season. He said he would be interested in returning the Nationals this offseason.
"I had a great time in Washington," Byrd said. "I still have friends over there. My boy [Ryan Zimmerman] is still handling things. Jayson Werth is there. I'm good friends with Michael Morse. They have some great people over there."
Based on what general manager Mike Rizzo has said since Spring Training, Byrd, 34, would not appear to be a long-term solution for the Nationals. As of now, the Nationals are looking for Bryce Harper to play the position in the future.