The Redskins released the receiver after unsuccessfully trying to trade him.
"I just heard. I just talked to Mike Shanahan. He said I was going to be making too much, and that they wanted to see what the other players can do," Gaffney told told ESPN's Josina Anderson on Tuesday.
"He said there is a chance I can come back, but he said it would be for around the minimum because I wouldn't be the starter anymore. I am not interested in going from being their leading receiver to being third-string, and having my number taken from me. That is pretty much telling me that I am not going to be making the team. Now Drew (Rosenhaus) can start talking to other teams to find me a new home."
Gaffney wore No. 10 in 2011 but new starting quarterback Robert Griffin III was given that number after being selected No. 2 overall in last week's draft.
The 31-year-old Gaffney led Washington in receptions (68), receiving yards (947) and touchdown receptions (5) in 2011 but the Redskins signed free-agent receivers Pierre Garcon and Josh Morgan this offseason and veteran Santana Moss also is scheduled to return to the team.