Washington is bring in a host of players on Thursday including TE Vernon Davis.
This is the first reported interest in Branch since the market opened.
Branch, 26, is a former second-round pick of the Jaguars back in 2012. He has played out his rookie contract and is now test the open market for the first time.
In 2015, Branch appeared in 13 games for the Jaguars and recorded 24 tackles, four sacks, two forced fumbles, one recovery returned for a touchdown and four pass defenses. Pro Football Focus has him rated as the No. 76 edge rusher out of 110 qualifying players.