The New York Yankees star played for the United States at the inaugural tournament three years ago, but chose to be with the Dominican Republic for this year's event.
"The only thing is I was upset about, Alex not, you know, being on my club," Johnson said Thursday, "I'm Madonna's fan. I was hoping she'd show up."
Rodriguez and Madonna were linked in tabloid reports last year as being very friendly.
The U.S. team opens March 7 against Canada. The Dominicans begin the same day against the Netherlands.
"I heard the reason he chose is his mother wanted him to play for the Dominican. So, I understood that," Johnson said. "I mean, it's not like, there's a huge drop-off. I mean, Chipper Jones and David Wright, those are great — I mean, I'm tickled to death to have those guys. I think that's his preference and that was his choice, and I respect that. That's fine."
At the 2006 tournament, the United States was managed by Buck Martinez and was eliminated with a 2-1 loss to Mexico in the second round. Japan defeated Cuba 10-6 in the final.
In addition to Canada, the Americans are grouped with Italy and Venezuela in a first-round group based in Toronto.
"I think the United States is the team to beat. Again, I think we came in a couple of years ago not fully cognizant on the competition around the globe and how prepared they were going to be coming into this," Johnson said. "I felt a lot of our guys weren't really ready to play, but I don't think that's going to be an issue coming in. ... What happened to us a couple of years ago sticks in the minds of a lot of guys and they don't want to see that happen. I think they're all pumped up and I think that's going to show in the way we play."
By holding the tournament in March, Major League Baseball and the players' association gain promotion for the start of the season. But it forces them to create artificial rules, such as pitch limits.
If the tournament were in November, after the World Series, it might see a level of play close to that of soccer's World Cup.
"I think that's true," Johnson said, "but I think it's also good to catch them when they're fresh."
Copyright 2009 The Associated Press.