Gulyás said an agreement on the purchase "has not been formally signed", but added that "with regard to the price, one could say, we are close to an agreement or have already reached one verbally".
The price agreed on is "favorable" and "in the lower range" of the price based on an estimate of the airport's value by an international consultancy, he said.
"The Hungarian government has made a good deal," he said and dismissed speculation that it would take "decades" for the price to be recouped.
He suggested that passenger numbers at the airport would continue to rise at a pace similar to that before the pandemic when the coronavirus crisis is over.
Gulyás said both sides "want to close the sale as soon as possible".
"That could be this year or early next year," he added.
Prime Minister Viktor Orbán said on Monday that the government could close the purchase of the airport "any minute now". If the state takes over the airport, developments could be undertaken that raise its stature "2-3 notches", he added.
Ferenc Liszt operator Budapest Airport is owned by AviAlliance (55.44%), a holding of Canada's Public Sector Pension Investment Board (PSP Investments); Malton, a subsidiary of Singapore's state investment fund GIC (23.33%); and Canadian pension fund Caisse du Quebec (21.23%).
The airport was privatised in 2005.
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