Westbrook, an unrestricted free agent, is scheduled to arrive in Denver on Wednesday night and spend Thursday meeting with Broncos officials and coaches.
On Wednesday, Westbrook met with Redskins head coach Mike Shanahan and offensive coordinator Kyle Shanahan, among others.
"He had a really positive visit with the Redskins," said Westbrook's agent, Todd France. "We're confident we're going to find the perfect fit."
Redskins general manager Bruce Allen called it "a good meeting" and that he will "probably have some meetings down the road" with the 30-year-old back.
Westbrook played eight seasons with the Eagles, usually in the backfield with new Redskins quarterback Donovan McNabb. He had two concussions last year and was released in February.
Westbrook has passed a physical with the St. Louis Rams, where he is familiar with offensive coordinator Pat Shurmur, a former Eagles assistant.
Westbrook's ailments that have passed physical screenings include knee and ankle injuries, as well as multiple concussions.
Adam Schefter is ESPN's NFL Insider. Information from ESPN senior NFL analyst Chris Mortensen and The Associated Press contributed to this report.