The rivalry could be going somewhere it has seldom gone before.

Cooperstown.

Yankees fans are almost certain to return to the National Baseball Hall of Fame in droves next July with the likely induction of Derek Jeter — and they could be seeing plenty of red there.

Former Red Sox pitcher Curt Schilling received the most votes from the Baseball Writers’ Association of America of anyone on the ballot not to get in this year with 60.9%. It wouldn’t take too big of a leap for the right-hander to get the needed 75% for induction. Right behind him was Roger Clemens, the hurler who spent the bulk of his career with the Red Sox and Yankees receiving 59.5% of the vote. Now that would be an interesting dynamic. It remains to be seen if the tiny town is big enough for the two rabid fan bases.

Jeter will likely be the only first-time member on the ballot to get in. Others eligible next year for the first time include left-hander Cliff Lee, along with first basemen Paul Konerko and Jason Giambi.

Jeter was in attendance Sunday to see fellow Core Four member Mariano Rivera get inducted as the first-ever unanimous member of the Hall of Fame. When asked by The Post’s Kevin Kernan if he was planning a return trip next year for himself, Jeter said: “Whoa, I’m not even going to go there.’’ But it would be very surprising if the .310 career hitter, five-time World Series champion and 14-time All-Star wasn’t inducted next summer.

“I’m looking forward to seeing Derek here [next year],” Rivera said. Asked if he should be unanimous as well, baseball’s all-time saves leader said: “Ask the writers. For me, he would get my vote. We’ll see.”

It would be ironic if Jeter is joined by Schilling, a 216-game winner with a 3.46 lifetime ERA and 3,116 career strikeouts who won 20 games or more three times and won three World Series titles during his 20-year career. He was partially responsible for arguably the most disappointing moment of Jeter’s storied career, the 2004 ALCS when the Red Sox rallied from 3-0 down to stun the Yankees and went on to end the Curse of the Bambino. He was also a key member of the 2001 Diamondbacks, who toppled the Yankees in the World Series in seven games.

Barry Bonds, baseball’s all-time home run leader with 762, received 59.1% of the vote in his seventh year on the ballot. His legendary career was stained by allegations of performance-enhancing drug use. Another intriguing name is outfielder Larry Walker. It will be the career .313 hitter’s final year on the ballot. He received 54.6% of the vote this year.