The aircraft landed safely at the airport, the source said.
The airline was operating the flight 9I 698 from Prayagraj to the national capital with an ATR 72-600, a twin-engine turboprop aircraft.
The source said the plane, which had around 40 people onboard, made an emergency landing as one of the engines was inoperative.
The aircraft landed at the Delhi airport around 2.15 pm, as per information available on flight tracking website Flightradar24.com.
There was no immediate comment from Alliance Air.