Also in the report, Rizzo said he personally saw Martinez thrown an inning in the Dominican Republic before the World Baseball Classic in March. The Nationals also scouted Martinez during the World Baseball Classic.
"Unless we got to a point where the price makes sense to us, we're very satisfied with what we've got in our rotation," Rizzo told FOXSports.com. "It's really young, but we think it's got a lot of upside.
"That [Martinez] would give us depth at the right number. We've kicked the tires a few times. But it hasn't really gone anywhere past that."
According to a Nationals team source, the club hasn't had interest in Martinez since Spring Training.
The only way the Nationals would sign Martinez is if he agreed to their parameters -- accept a cheap contract and be a mentor to the young starting rotation, which has a 2.27 ERA in its last seven games. According to published reports, Martinez wants a one-year, $5 million contract. That will not happen in Washington.
"We are satisfied with our rotation even though there is going to be some bumps along the way. We wouldn't want to make any changes there." the source said.
Martinez, 37, went 5-6 with a 5.61 ERA in 20 starts for the Mets last season, his first full season coming off shoulder surgery. He has worked only 269 2/3 innings over the past three seasons.
He pitched twice for the Dominican Republic against The Netherlands in the World Baseball Classic, pitching six scoreless innings.
The report states Martinez has been working out regularly in the Dominican since the tournament, but mostly playing long toss and that his return to the mound is a strong indication that he is preparing to return to the Major Leagues in the near future.
Martinez is reportedly asking for at least $5 million on a one-year deal. The Dodgers, among other clubs, have maintained that they are not interested in Martinez at that price.
FoxSports.com said Martinez is looking to join either a contender or a rebuilding club that would want him to lead its pitching staff and serve a mentoring role. The report also states Martinez has told some friends that the Yankees are interested, but a team source told the Web site, "There is no truth to that -- zero. We have no interest."
The Nationals could afford Martinez if he indeed was willing to pitch for a lesser club and willing to reduce his price, the report said. The Indians, who offered Martinez a contract in December, no longer have the financial flexibility to sign him. The Mets are also not interested.
The report describes Martinez as a potential draw for Washington, a team struggling to build a fan base. Martinez has a good relationship with Nationals manager Manny Acta, who managed the Dominican Republic in the first World Baseball Classic. Additionally, Martinez could help the Washington restore its image in the Dominican Republic. Former Nats general manager Jim Bowden and special assistant Jose Rijo are subjects of a baseball investigation in the Dominican and the franchise has shut down its academy in the Dominican while restructuring their Latin American operations, according to ESPN.com.