That wasn't the case last year, when he realized a dream by representing his native Brazil in the World Baseball Classic. The right-hander's WBC duties took him to Japan for the first round of the tournament in early March and by the time he got back he had to readjust his energies toward his real job.
Rienzo wouldn't trade in the experience for anything and he ultimately reached the major leagues at the end of July, taking over a White Sox rotation spot when Jake Peavy was traded.
There were flashes of solid pitching and some struggles as Rienzo fought through command struggles, but he still returned this winter to tell tales of joy in his native Brazil where the temperatures were "hot, hot, hot," as he put it.
"It was great, you know," the 25-year-old said. "The people in Brazil know that baseball is not popular and soccer is the sport. But the people who know baseball are happy with me and glad that I can finally go to the major leagues after seven years in the minors. They were so happy and it was just for two months. I don't know the future yet, but I know what happened and the people are happy."
Looking through the clubhouse now, the faces are even more familiar than they were before. And Rienzo has already made fast friends with one of the new players since the two have a little history together.
Rienzo, is not only fluent in English and his native Portuguese, he can also speak Spanish and was able to have an early-spring chat with new first baseman/designated hitter Jose Abreu. The two faced each other in the WBC last year with Rienzo getting Abreu to fly out to right field two times. Abreu got the last laugh when his team won an unexpectedly tight 5-2 victory.
"I talked to him before because I recognized him," Rienzo said. "I said ‘Hey man, do you remember me from Brazil?' He said, ‘Yeah, hey man. Hey, good pitching." I talked to him a little bit and I told him now we're on the same team and friends so forget it."
When it comes to Opening Day on March 31, though, remaining on the same team will be a challenge. Abreu is expected to make it but Rienzo will have a challenge. There are two open rotation spots, but Erik Johnson appears to be in the lead for one of those spots, while Felipe Paulino could take the other if he proves that he is recovered from elbow and shoulder procedures over the past year and a half.
"I just try to work hard," Rienzo said. "I want to be there but that is not my decision it's the boss' decision. What is in my hands is to work hard and do my work so that's what I will do."
The White Sox coaching staff will have a little more to go on this year when it comes to judging Rienzo's talent. He made 10 big league starts in 2013, with six of those considered quality starts. But he posted a 4.82 ERA and showed control issues that he will have to fix in order to get another chance.
"He came up early on and did great and the energy he brings and how he prepares is fine," manager Robin Ventura said. "I think he ran into a period where command just became an issue and you can't have that. Anytime a guy doesn't have command it becomes a lot more difficult for you and the team."
Rienzo said the issue has been addressed even before arriving to the desert.
"This winter I was working on something [pitching coach Don] Cooper told me last year," Rienzo said. "He said if the ball is up you won't have a long life here. I worked on getting down, down, down. Get the ball down to have more life.
"I don't know the future. It's in the boss' hands. If I go, I go. I can only do what I can do. If I don't go I will still work hard to go soon. But it's my fault because I need to keep the ball down to have more time on the mound and help the team."