But that was actually a possibility, according to the iconic closer himself.
"It was real," Rivera said at Yankee Stadium on Thursday, two days after his two-year deal was officially announced.
There were no formal face-to-face discussions with the Red Sox, but there was definite interest, said Rivera, who "made sure that I thanked them, because they took me into consideration. But, again, this is business, and the Yankees did the right thing. And I'm here."
Perhaps more so than acquiring ace left-hander Cliff Lee, the Yankees went into this offseason with a focus on making sure Rivera and captain Derek Jeter stayed put. Unlike the Jeter negotiations -- which eventually developed into a public back-and-forth between the front office and agent Casey Close -- the Rivera discussions were handled rather quietly and easily.
But there was one wrinkle: The Red Sox were after him, too.
ESPN.com reported recently that Boston, which has Jonathan Papelbon as its closer, offered Rivera essentially the same two-year, $30 million deal he signed with New York, with WEEI.com stating that it was Rivera's representative, Fernando Cuza, who initiated contact with the Red Sox.
"It would've been different," Rivera said.
But was there ever a point when Rivera felt pitching for Boston could happen?
"I don't think so. I don't think the Yankees will allow that to happen," he said while making an appearance for the 17th annual Yankees holiday food drive. "I just had to make sure that I had a job, and the Yankees did that."
The Yankees did, and despite the uncertainty they currently face in their starting rotation, the ninth inning continues to be a strength in the Bronx -- which has been the case since Rivera became the full-time closer in 1997.
Rivera, who ranks second in career saves with 559 and is just 42 behind all-time leader Trevor Hoffman, is 41 now and will turn 43 shortly after this current deal expires. But that filthy cutter hasn't aged a bit, and the 2010 season was just as dominant as any in Rivera's eventual Hall of Fame career. So whether or not this is actually his last contract is a legitimate question.
Rivera doesn't know for sure.
"I've been saying that for the last, what, eight, 10 years? But I'm still here," he said. "So it's a blessing. It's a blessing, and I thank God for that. I just have to continue doing what I have to do."
Rivera has averaged 40 saves a season over the last 14 years. Signed by the Yankees out of Panama in 1990, Rivera was initially a starter but evolved into arguably the greatest closer of all-time. He sports a career 2.23 ERA and has converted 89 percent of his save chances during the regular season. In 94 postseason games, he is 8-1 with an all-time-low 0.71 ERA, a record 42 saves and five World Series rings.
In 2010, the 11-time All-Star posted a 1.80 ERA in 61 appearances and notched 33 saves, becoming the only pitcher in Major League history to record at least 30 saves in 13 seasons.
"I was glad that everything was set up nice and easy," Rivera, currently the longest-tenured Yankee, said about his negotiations. "We got it done and move on."
Since Lee chose the Phillies, the Yankees must address a starting rotation that has serious questions after the first two spots. Rivera said he "was surprised like you were surprised and everybody else" that Philadelphia got involved, saying he felt New York "had a good shot" to sign Lee.
"You just can't sit down here and cry," Rivera added. "You have to move on, simple as that."
Now that he has re-upped with the Yankees, Rivera will move on in his own way. His next mission: Get a feel for Andy Pettitte's situation.
Pettitte, 38, still hasn't decided whether he'll retire or come back for a 17th season. But considering the Yankees' rotation issues and the left-handed-hitting additions the Red Sox made with Adrian Gonzalez and Carl Crawford, the veteran southpaw would be a welcome presence in New York.
Rivera said he'll reach out to Pettitte soon. And if retirement is where he's leaning, Rivera may try to sway him in the other direction.
"I might," Rivera said. "He will have the last word, but I might. Andy, to me, is one of the best lefties that we have out there. So I would take him any time."
Yankees general manager Brian Cashman and manager Joe Girardi said nothing has changed on the Pettitte front yet, though Jon Heyman of SI.com and MLB Network wrote recently that Pettitte is leaning towards a return.
Girardi spoke to Pettitte earlier this week, but he still doesn't know which way the southpaw is leaning.
"I still think he's just weighing his options and seeing what his heart is going to tell him," Girardi said. "I think he's taking his time to make sure that he makes the right decision. I can't tell you whether he's going to play or not going to play, but there is communication there. I think everybody knows our feelings on Andy Pettitte. We'd love to have him back, but he has to want to come back and pitch again."
Alden Gonzalez is a reporter for MLB.com and writes an MLBlog, Gonzo and 'The Show'. Follow him on Twitter @Alden_Gonzalez. This story was not subject to the approval of Major League Baseball or its clubs.