Hernandez said he did not ask for a lot of money, but he did not say how much he was seeking.
Rizzo did not respond to an e-mail asking to confirm that such a proposal was given to him.
"[My agent and I] sent a proposal," Hernandez said. "I'm waiting for Rizzo to call me back, so I don't know what's going on. I called him a couple of times, and he never called me back. I want to go back to the Washington Nationals.
"When I call people, I would like them to respond to my phone calls and talk to me. Sometimes, it's very disappointing and frustrating. ... I want to show that I can help the team win. It's better now by signing Ivan and a couple of more guys."
Hernandez is coming off a disappointing 2009 season in which he went a combined 9-12 with 5.44 ERA for the Mets and Nationals. Washington signed Hernandez as a free agent on Aug. 26, six days after the Mets released him.
Bill Ladson is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.