Orban instructed the minister responsible for state assets to conduct the talks and inform the cabinet about the results by June 30, the gazette said.

The government bought Budapest Bank from the financial arm of General Electric in 2015 for $700 million (534.39 million pounds).

Hungary has targeted at least 50 percent domestic ownership in the banking sector, a key plank in Orban's economic policy which has prompted speculation that Budapest Bank will end up in domestic hands.

Orban's business allies have made significant inroads in the banking sector in recent years, acquiring controlling stakes in MKB, one of the largest banks in the country, as well as FHB mortgage bank and the savings and loan cooperative Takarekbank.

The bank sector's runaway leader in Hungary is home-grown regional heavyweight OTP Bank, which has expanded in Central Europe rapidly in recent years and made record profits of about 1 billion euros in 2017.

Aside from OTP and MKB, Budapest Bank competes in Hungary with Austria's Erste Group Bank and Raiffeisen, Belgium's KBC Group and Italy's UniCredit and Intesa SanPaolo.

(Reporting by Marton Dunai and Sandor Peto; Editing by Kevin Liffey and Mark Potter)