He, however, said that a favourable deal would be ensured for all the employees.
"I will go to that extent and say that," the Minister said replying to a question in the Upper House.
Taking a small pause Puri said that the airline would be closed down if not privatised.
The government is readying the bid document for selling off its entire stake in the national carrier and has set March 31 as deadline for completing the disinvestment process. In earlier attempt, the Modi government had in May, 2018 invited the expression of interest (EoI) to sell 76 per cent of its stake but not a single private party showed interest in the first stage of bidding.
The top aviation ministry officials and Air India Chief Ashwani Lohani are currently meeting the potential investors before launching the bid process.
Hardeep Puri had last week said that the Group of Ministers (GoM) on Air India had earlier met and taken some decisions.
Asked by a member in the Rajya Sabha if pilots had been leaving the airline in the wake of privatization, the Minister replied in negative.
Air India has stayed afloat on government support. The UPA-II government had cleared a financial package of over Rs 30,000 crore to ensure the public sector carrier survived.
( With inputs from IANS )