Rodriguez caused a stir after playing for the Dominican Republic on Tuesday, saying he would like to see Mets shortstop Jose Reyes at the top of the Yankees batting order.
"I wish he was leading off on our team and playing on our team," Rodriguez said. "That's fun to watch, any time you have that type of speed. We have a guy in (Brett) Gardner. That'll be fun. That's probably the most fun you can have -- watching a guy like that run."
Rodriguez said he wasn't disrespecting his New York Yankees teammates.
"Everything that comes out of Alex's mouth now days is going to be scrutinized," Damon said before the Yankees played the Atlanta Braves on Wednesday.
"I'm not going to let that bother me, and I hope Derek doesn't go that way either," Damon said. "We all know Jose Reyes is a great player, a great leadoff guy. He's a great player who might have 10 or 15 more years left in him. Yeah, I think there's probably 25 other teams who would want him to lead off and play short."
Jeter worked out at Steinbrenner Field before leaving to join the United States for a game Wednesday against Toronto.
"I've got nothing to say, man," Jeter said.
Damon joked that when Rodriguez rejoins the Yankees, he was going to "go out there and prove to Alex what I can do."
"I'm sure when you walk into the clubhouses of WBC teams, players start to get a little giddy," Damon said. "Look at all theses great players around."
Damon is in the final year of his $52 million, four-year contract.
"I've been able to do this for going on my 15th year," Damon said. "I've been around and done some pretty good things in this game, and I feel like I still can. Hopefully I have five more in me."
Rodriguez was scheduled to have a cyst on his right hip examined Wednesday.
"He's a very good player, but we also have a lot of depth this year," Damon said. "If Alex can't go, we have Cody Ransom, who is probably the best athlete on the team. No one can really do what Alex can do, but we'll move forward."