Rivera, 42, was seen by specialist Dr. Russell Warren, as well as team physician Dr. Chris Ahmad, at the Hospital for Special Surgery, Yankees general manager Brian Cashman said.
"We ran into complications,'' agent Fernando Cuza told the New York Post, explaining why surgery was not scheduled. "I am referring to Dr. Ahmad and Brian Cashman for further information.''
Cashman said, according to the Post: "I won't comment on that right now."
The Yankees were not anticipating that the two doctors would have a different opinion than the one that was reached in Kansas City, where Rivera was told he tore his ACL, as well as some of his meniscus, while shagging fly balls in the outfield.
"They're gathering all that information, and we'll go from there," Cashman said.
Rivera has vowed to pitch in 2013. He could have surgery within the next month after swelling subsides and resume a throwing program within four to five months.
In the meantime, Cashman said that he believes the Yankees' bullpen needs can be covered from within. David Robertson figures to pick up most of the save opportunities in Rivera's absence, with Rafael Soriano also receiving calls in the ninth inning.
"I always try to look from within in-season for our answers," Cashman said. "Obviously we have closer candidates in Robertson and Soriano, so I think we have guys that can step in and try to fill in."
Cashman said that, in the wake of Sunday's strong outing at Kansas City, he is not inclined to shuffle Phil Hughes from the rotation to stabilize the sixth or seventh inning behind Soriano and Robertson.
"I'd rather not take any of our starters and put them in the bullpen just to reinforce the sixth or seventh innings," Cashman said. "I'd rather not do anything like that."