Thames, who was available as a pinch-hitter in Friday's 2-1 win over the Mets, planned to test his ankle by running in the outfield before Saturday's game.
"I'll got out today and see what I've got," Thames said.
Thames was announced as a pinch-hitter in the eighth inning of Saturday's 5-3 loss but was replaced by Juan Miranda when the Mets brought in right-hander Fernando Nieve to replace Pedro Feliciano, a lefty.
A day after Kevin Russo started in left field and had two hits, including a two-run double, Randy Winn got the starting nod on Saturday.
Thames last played on Wednesday, when he left a loss to the Tampa Bay Rays after tripping on his own bat while running to first base on a single. He said the swelling in the ankle had disappeared.
"There was a little bit yesterday," Thames said of the swelling. "But today, I got some treatment. It feels better. Hopefully, I can go out there and put my weight on it."
"He's available to me," manager Joe Girardi said. "He's made progress. As far as being an outfielder, I probably wouldn't do that. If he hit for me, I might even pinch-run for him."
Before Thames returns to the outfield, he'll need to prove his ankle can stand the starting and stopping required of playing a corner-outfield position.
"The biggest thing is making cuts and stuff on it," Thames said.
With the Yankees set to face left-hander Johan Santana on Sunday night, an available Thames would help the lineup. In his career, the right-handed batter has hit .235 with a .295 on-base percentage against righties but .263 with a .337 OBP and a .521 slugging percentage against lefties. In 71 plate appearances this year, Thames has hit .357 with a .465 OBP and two home runs.
-- Thomas Boorstein