Davis has played for the Redskins since being drafted by the team in 2008, and he met earlier in the week with the Bills.
He was the Redskins' leading receiver with 24 catches for 325 yards before tearing his Achilles tendon against the Giants this past October.
He recently told the NFL Network that he is recovering well from the injury and that he is even "a little bit ahead of schedule."
Davis also said his preference was to remain with the Redskins, but that he was open to signing with another team.
"I definitely would [like to stay], but at the end of the day, I'll play wherever," Davis told the NFL Network. "It doesn't matter to me. It's about football to me. I would like to stay here, but if I can't, I'm fine with that as well."
In 2011, he was having a career year with 59 catches for 796 yards before being suspended for the final four games after failing multiple drug tests.
The 27-year-old tight end has 155 catches, 1,973 yards and 12 touchdowns in 62 career games.