There is no such proposal before the board, both companies said in separate exchange filings.
There has been speculation the two companies may be combined if Sesa Sterlite, the merged entity of Vedanta Group firms, acquires the government's residual 29.5 percent stake in the zinc producer.
Vedanta has a 55 percent stake in Sesa Sterlite, which holds a 65 percent stake in HZL.
Earlier this week, the Cabinet Committee on Economic Affairs approved the sale of the government's stake in HZL, currently valued at over Rs 16,500 crore. It sold a majority stake in the nation's largest zinc maker to Vedanta in 2002.
The decks for the sale were cleared following the Attorney General's view that there would be no problem in offering the stake through an auction since HZL is no longer a public sector company.
The sale might help the government garner more than the budgeted Rs 14,000 crore from the sale of its residual stakes in companies in the current financial year. It may also help the government to meet its fiscal deficit target of 4.8 percent for the year.
The mining conglomerate had taken the approval of its shareholders last year to make offers of up to Rs 21,637 crore for buying stakes in HZL.