Martinez said the Phillies have been scouting him in his native Dominican Republic.
"The Phillies saw me this past Tuesday in a simulated game and I felt very good with my fastball and all my pitches," Martinez said Thursday.
Phillies general manager Ruben Amaro Jr. denied reports a deal was done, but confirmed the team's interest in the three-time AL Cy Young Award winner.
"He has not been signed," Amaro said before the NL East-leading Phillies played Cincinnati on Thursday night. "We've seen him pitch. He's not in town."
The Phillies have asked Martinez to throw for them a second time to see how his arm responds, a source told ESPN.com's Jayson Stark. Martinez initially balked at the idea, the source said, believing the Phillies had enough information to make a decision from his simulated game Tuesday.
Martinez has since agreed to work out again, at 1 p.m. ET Friday at the Phillies' complex in the Dominican Republic, a source told ESPNdeportes.com. If it goes well, the source said, Martinez would travel to Philadelphia on Monday.
If the Phillies conclude a deal with Martinez, it will not keep them from continuing conversations with the Blue Jays about Roy Halladay, National League sources told ESPN The Magazine's Buster Olney.
The 37-year-old Martinez is reported to have worked three innings in a simulated game against a Phillies summer league team, with his fastball clocked at up to 93 mph.
"I feel the best I have for some time," Martinez said.
The eight-time All-Star said it was up to his agent and the defending World Series champion Phillies to wrap up contract details.
Martinez went 5-6 with a 5.61 ERA for the New York Mets last year. The free agent pitched in the World Baseball Classic before this season started.
The Phillies have been hurt by injuries to their starting rotation. No. 2 starter Brett Myers had hip surgery in June and his replacement, Antonio Bastardo, landed on the disabled list after making five starts. Philadelphia already has used nine starters through 82 games. The Phillies used only seven starters last season.
Martinez is 214-99 with a 2.91 ERA in 17 seasons with the Los Angeles Dodgers, Montreal, Boston and the Mets. He helped the Red Sox win the World Series in 2004.
ESPN The Magazine senior writer Buster Olney, ESPN.com writer Jayson Stark, ESPNdeportes.com reporter Enrique Rojas and The Associated Press contributed to this report.