"We support our teammates. We can't turn our backs on them," said Rivera on Monday. "He will be the person to talk more when the time comes. All I do is just pray for him and make sure he's OK."
The Yankees held a charity event at the Hard Rock Cafe in Times Square to support Carlos Silva, a producer for the club's radio broadcasts who is battling cancer.
More than $20,000 was raised by the event, which also featured appearances by first baseman Mark Teixeira, general manager Brian Cashman and manager Joe Girardi.
Teixeira agreed that the team would support Rodriguez, but also took a firm stance during a Q&A session with fans when discussing the topic of performance-enhancing drug use.
"There's no place for it in our game," Teixeira said.
Cashman said he could not comment extensively on Rodriguez's situation while Major League Baseball looks into any potential links between Rodriguez and South Florida-based biochemist Anthony Bosch, who is alleged to have provided PEDs for the 37-year-old slugger.
Through his attorneys, Rodriguez has denied the charges, saying he has never had a relationship with Bosch. Cashman said he has not spoken to Rodriguez, and that "in terms of this issue, no one from the Yankees has spoken to Alex."
Girardi said he has communicated with Rodriguez, but only concerning his rehab from left hip surgery.
"Right now, it's baby steps," Girardi said. "He's not that far from just having surgery. I saw him at the park and he was doing exercises, riding a bike. The rehab is going, and that's good."
Cashman said it would be "premature" and "negligent" for the Yankees to comment publicly on MLB's investigation, which he said realistically cannot be expected to be concluded quickly.
"This is an ugly story that we wish didn't exist, but it's there, and so we'll take the time to let it process," Cashman said.
Cashman and Girardi said they were not certain if Rodriguez would be with the team on Feb. 15, when position players are expected to report to camp in Tampa, Fla., but Girardi said he doesn't believe Rodriguez's presence will be a problem.
"I think our club is used to handling distractions, with the city we play in," Girardi said. "There's a lot of news always surrounding our club. A lot of times, it's a lot of good news, too.
"Our club will handle it. As a club, you're going to go through adversity all the time. Going through a season is never easy. Why would this year be any different?"