(Adds detail) BUDAPEST, Nov 15 (Reuters) - The owners of Budapest Airport have entered into a due diligence process with the Hungarian government, its majority shareholder said on Monday, potentially the first step towards a sale of the asset to the state. Prime Minister Viktor Orban, a nationalist often at loggerheads with the European Commission, has said for months that he wants to see the airport in domestic hands, but its owners had so far expressed no interest in selling it. Local media reported late last month that Hungary had offered 4.44 billion euros ($5.08 billion) for the airport, a figure which neither its biggest shareholder AviAlliance GmbH, formerly Hochtief AirPort GmbH, nor the government confirmed. But AviAlliance confirmed on Monday that a consortium led by the Hungarian government had submitted a revised non-binding offer to buy the airport. “The Hungarian government has accepted our terms and conditions for starting formal negotiations. Therefore we have decided to enter into a due diligence process,” AviAlliance said in a statement. “While this is potentially the first step towards the sale of the airport, we want to emphasise that the outcome of such a process is not predetermined.” Since 58-year-old Orban took power in 2010, his government has boosted Hungarian ownership in strategic sectors such as energy, banking and the media. Orban, who faces a closely fought election next year, told a party congress on Sunday that his government would buy back the airport and carry out investments in the fast-growing hub that had benefited from a boom in low-cost travel before the pandemic. AviAlliance, which holds a 55.44% stake in the airport, is owned by Canada’s Public Sector Pension Investment Board (PSP Investments). Singapore’s GIC Special Investments and Canada’s Caisse de depot et placement du Quebec (CDPQ) each hold a little over 21%. $1 = 0.8743 euros Reporting by Gergely Szakacs; Editing by David Evans and Jan Harvey