The Spaniard, a double world champion, said he wanted one day to emulate Graham Hill, the late Briton who won the Formula One title, Indy and the Le Mans 24 Hours sportscar race in the 1960s.
The appeal of competing in the "greatest spectacle in racing" will only have been increased by his Honda-powered Formula One team's current woes - McLaren is last in the championship after two races without a point.
"I’ve won the Monaco Grand Prix twice, and it’s one of my ambitions to win the Triple Crown, which has been achieved by only one driver in the history of motorsport," Alonso said in a team statement released ahead of this weekend's Bahrain Grand Prix.
"It’s a tough challenge, but I’m up for it. I don’t know when I’m going to race at Le Mans, but one day I intend to. I’m only 35: I’ve got plenty of time for that."
McLaren will enter the 101st edition of the Indy, on May 28, with a Honda-engined Indy car run by Andretti Autosport, owned by former McLaren driver Michael Andretti, in the old papaya orange livery of the 1970s.
It will be the first time in 38 years that McLaren have competed at The Brickyard. They won at Indianapolis in 1974 and 1976 with Johnny Rutherford, while Hill did so in 1966.
The other Formula One champions to have won at Indy are Britain's Jim Clark, American Mario Andretti, Brazilian Emerson Fittipaldi and Canadian Jacques Villeneuve.
Alonso is out of contract with McLaren at the end of the season and speculation has risen about whether he will see out the year at a team that have slipped far from their glory days.
The second most successful team in the sport after Ferrari, in terms of race victories, have not won anything since 2012 and has been well off the pace since starting a new partnership with Honda in 2015.
"I’ve never raced an IndyCar car before, and neither have I ever driven on a super-speedway, but I’m confident that I’ll get to grips with it fast," said Alonso, who will fly to Indianapolis immediately after his home Spanish Grand Prix.
McLaren said they would name a replacement in due course for Monaco, a tight and twisty circuit which promises to be trickier than usual with the 2017 cars wider than before.
Britain's 2009 world champion Jenson Button, a former Monaco winner, remains contracted to McLaren despite handing over his seat to Belgian rookie Stoffel Vandoorne last year. –Reuters