He said the government would have to bring a "transformation" in Air India to make it a "good" airline.
The government's think-tank NITI Aayog has proposed total privatisation of the national carrier, which is sitting on a debt pile of Rs 52,000 crore.
However, Union Finance Minister Arun Jaitley has favoured disinvestment of the loss-making carrier.
Addressing a press conference here today, Sinha, who is the Minister of State for Civil Aviation, said the government is currently deliberating on the issue of ownership of Air India and Cabinet will take a decision in this regard.
"The current numbers suggest that our airlines are running in profit. They are not running in losses. Even Air India too is in profit," he said.
Air India, which is surviving on a Rs 30,000 crore bailout package spread over 10 years announced by the Manmohan Singh government in 2012, is working on ways to improve its financial position.
In 2015-16, the airline posted operational profit of Rs 105 crore on account of low fuel prices and increased passenger numbers.
"We are fortunate that oil prices have come down. The cost of aviation turbine fuel has come down 40 to 50 per cent and because of that flying has become affordable," Sinha said.
He said the government has undertaken efforts to further bring down various charges, including those related to airport and landing.
Observing that the aviation sector has seen growth, the minister said that air tickets have become cheaper and affordable, as a result of which the common man too is flying.
"As far as the passenger trips are concerned, in the last three years, there is a 70 per cent rise. So it is wrong to say that the aviation sector is running into losses, in fact they (airlines) are in profit," he added.
Sinha said there are currently 500 commercial jets in the country and more than 850 new jets are on order.
"The new order has been placed because they are in profitable business and sustainable too," he said.
Responding to a query, the minister said that government aims to make Air India a "great global airline".
"We want to make Air India a great global airline and to make it happen, we need to transform it.
"We will have to change the operations, we will have to alter balance sheets, we will have to change the product's quality and we will have to make changes in route network also," he said.
He said through the regional connectivity scheme 'UDAN', smaller cities are being connected to the aviation network.
"The air fares too are becoming cheaper. We are also working to bring down the cost in the aviation sector to make it sustainable.
"We have also put a price cap in UDAN scheme to make the ticket more affordable to the common people. Our aim is to connect 200 more airports in the next few years as our goal is to provide airport to every person within the radius of 150 km," he said.
When asked about the expansion of existing Lohegaon airport in Pune, Sinha said there is good coordination between the Air Force and the Airport Authority of India when it comes to acquiring more land for the civil airport.
He said they are also working on the extension of the runway at the airport.
"We have the runway of about 2 km on which we can land narrow body planes, which have flying range of about 5 hours but if we have to get to Frankfurt or London, we need to be able to land long haul jets. For that we need runway of three km and to acquire land, the discussions are going on," Sinha said.
On the proposed international airport for Pune near Purandar, Sinha said the whole process will take five to six years.