Pawan Hans -- where the Centre and ONGC hold 51 per cent and 49 per cent stake, respectively -- has more than 900 employees, including 450 on permanent roll.
The union claims to represent around 300 employees of Pawan Hans.
In a letter dated August 7, the union has suggested that Pawan Hans be merged with ONGC or made a subsidiary company by way of increasing ONGC's stake to 51 per cent.
After ONGC hikes the stake to 51 per cent, Pawan Hans can go for public issue "to get the government a much higher price from the sale of shares... In the next five years with expansion and improved performance", the letter stated.
"Once Pawan Hans Ltd becomes a subsidiary of ONGC, its market value shall be two to three times higher based on its linkage to ONGC share prices," it added.
In October last year, the Cabinet Committee on Economic Affairs (CCEA) had given its in-principle approval to strategic disinvestment of profit-making Pawan Hans.
Set up in 1985, Pawan Hans has a fleet of over 40 helicopters.