The order includes A320neos and A321neos, the source said. Airbus declined to comment.
The deal is expected to be officially announced later Wednesday at the Dubai Air Show, they added. The aviation giant is expected to hold a press conference around 1000 GMT.
The order, believed to be the biggest ever for Airbus, will more than double the value of the airline’s sales for the year.
The airline had announced orders for 288 planes as of the end of October.
It will also allow Airbus to overtake Boeing, with a total of 718 orders against its American rival’s 605.
Indigo Partners is a US investment firm founded by Bill Franke that specialises in the lease of planes to low-cost airlines.
The A320neo and A321neo jets feature new generation engines that use 15 percent less fuel compared to their peers.
The deal marks a major coup for Airbus’s Chief Operating Officer John Leahy, who is expected to leave the group soon at the end of a career in which he oversaw the sale of nearly 15,000 planes.