Doug O'Neill, the Californian-based trained of I'll Have Another, wasted no time declaring his intentions to run the three-year-old in the remaining two legs.
Speaking to reporters outside the winning colt's barn at Churchill Downs on Sunday morning, O'Neill said it was all systems go for the Preakness Stakes on May 19 and the Belmont Stakes on June 9.
"It's pretty darn exciting to think about," O'Neill said.
"He's just a special horse, obviously. I think he has a chance to be something that hasn't been done in a long time."
O'Neill had originally planned to keep I'll Have Another at Churchill Downs for another week but said he now planned to travel to Maryland on Monday to get acclimatised to the Pimlico track.
It has been 34 years since Affirmed in 1978 became the last horse to complete the Triple Crown. The last horse to win the Kentucky Derby and Preakness was Big Brown four years ago.
"We're going to the Preakness, baby," said O'Neill.
The field for the Preakness will not be decided until just a few days before the race but only a handful of the 20 horses who contested the Derby are expected to back up.
Bodemeister, the 4-1 Derby favourite who finished second after trying to lead all the way, is likely to run again as long as he stays fit.
"I'm going to wait until next week to decide what to do with him," Bodemeister's trainer Bob Baffert said. "If he tips me off, we'll go."
The connections of the third-placed finisher Dullahan were considering skipping the Preakness and saving their horse for the final leg in New York.
Trainer Graham Motion, who won last year's Derby with Animal Kingdom and was fourth on Saturday with Went The Day Well was considering the Preakness as were the connections of fifth placed Creative Cause.
Michael Matz said Union Rags, who finished seventh after getting caught in heavy traffic, would also skip the Preakness and concentrate on the Belmont while the Florida Derby winner Take Charge Indy, who finished second last, would be out of training for at least two months after chipping a small bone on his front ankle.