The two GCC banks are part of five lenders vying for a share of Egypt's Alwatany.
Egypt has asked five banks from Greece, Kuwait and the United Arab Emirates to conduct due diligence on Alwatany Bank of Egypt and offer to take over the lender, Dubai-based al-Bayan daily said on Monday.
National Bank of Kuwait, Dubai-based Mashreqbank, National Bank of Greece, Bank of Greece and EFG Eurobank are on the Egyptian central bank's shortlist of bidders, Bayan quoted banking sources as saying.
Officials at Alwatany bank declined to comment.
Officials at National Bank of Kuwait were not immediately available for comment. The bank has been seeking a presence in Egypt, the most populous Arab country, and said in February it was in talks to buy into Egyptian Gulf Bank or another lender.
A Mashreqbank spokeswoman said she could not comment immediately on the report.
A Mashreqbank consortium made an unsuccessful bid for Egypt's state-owned Bank of Alexandria, which was privatised last year. Chief Executive Abdul Aziz al-Ghurair said in March Mashreqbank was considering other targets in Egypt.
Banque Saudi Fransi, Kuwait Finance House and Qatar Islamic Bank had also expressed interest in the Egyptian bank, al-Bayan said.
Egyptian financial newspaper Al Alam Al Youm said on May 21 five financial institutions had the central bank's permission to do due diligence on Alwatany.
That report, which cited Alwatany Chairman Ayman Fathi Hussein, did not name the bidders.
Alwatany had a market value of 3,466.5 million Egyptian pounds ($608 million) at the end of the last session.