Non-tendered by the Nationals on Friday, the 30-year-old is attracting interest from about 10 clubs, according to an MLB Players Association source.
The Orioles are "showing a lot of interest," the source added. The Mets also are in the mix.
With Washington the past two seasons, Redding proved durable in 2008, making 33 starts while logging 182 innings. He was 10-11 with a 4.95 ERA, and he posted 120 strikeouts.
Baltimore also has expressed mild interest in right-hander Carl Pavano. But its main focus is on Redding.
The source added that if a team steps up with an aggressive offer, a deal involving Redding could be reached by the end of the week.
Redding broke in with the Astros in 2001. He has appeared in 149 MLB games, with 127 starts.
Joe Frisaro is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.