The development also comes at a time when no-frills carriers- IndiGo and GoAir- have grounded at least 11 A320 Neo aircraft due to problems in their Pratt and Whitney (P&W) engines.
Airbus 320 Neo- the new engine option- are more fuel efficient and Indian carriers have placed orders for more than 500 such planes.
The A320 Neo planes of Air India and Vistara are powered by CFM-made engines while those of IndiGo and GoAir run on P&W engines.
The sources told PTI that Air India has deferred the delivery of at least one A320 Neo plane due to problems with CFM engine- probably the first instance of these planes facing woes on account of CFM engine.
Specific details could not be immediately ascertained. Queries sent to Air India spokesperson on Thursday remained unanswered.
When contacted for comments about Air India deferring the delivery of aircraft on account of CFM engine issues, a spokesperson for Safran Aircraft Engines in an e-mailed statement said, "I regret to inform you that CFM does not want to comment."
CFM is an equal joint venture between US-based GE and France's Safran Aircraft Engines. It manufactures LEAP and CFM56 engines for commercial planes.
"We are working closely together with the engine makers and our customers on next deliveries, which are agreed with the customer," an Airbus spokesperson said in an e-mailed statement.
The aircraft for Air India are powered by LEAP-1A engine manufactured by CFM.
The national carrier took delivery of the first LEAP-1A- powered A320 Neo aircraft earlier this year. Air India has plans to lease a total of 27 A320 aircraft, including Neos. Air India has a fleet of 112 planes.
Recently, Civil Aviation Minister Ashok Gajapathi Raju said technical snags faced by A320 Neo aircraft operated by IndiGo and GoAir pose a "safety issue".
"Obviously, any failure is a safety issue. So, the operating procedure we changed... What is attractive is fuel efficiency. Fuel efficiency is one thing and risking life is another," the minister had told PTI in an interview.
His comments had come in response to a query on whether the P&W engine issues were a safety concern.
The aviation regulator DGCA has asked the American engine maker to expedite the supply of spare engines to India.
On whether there could be harsher action with respect to the engine issues, Mr Raju had said some of the planes have been grounded because of regulations, implying that existing norms are strict.
"Why are they grounded, that is because of the regulations. You don't want to take risks with life... Everybody is working on it (addressing the engine issues). As long as glitches don't massacre human beings, it is okay. They will be addressed and sorted out," he had said.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)