The Seattle Mariners are reportedly looking to bolster their outfield depth.
Byrd is hitting .263 with 18 home runs and 54 RBIs for the lowly Phillies, and would be a major upgrade over Endy Chavez and Corey Hart in right field for the Mariners.
The Kansas City Royals are also rumored to be interested in the 36-year-old's services.
Byrd will make $8 million over the next three seasons and won't be a free agent until 2017.