The two lenders have been in merger talks since mid-2018.
The Chief Executive of Kuwait Finance House (KFH) has announced that a decision on the share pricing of a potential merger with Bahrain's Ahli United Bank (AUB) will be reached within two weeks, reported Reuters.
If the tie-up between KFH and Ahli United Bank materialises it will be the first cross-border merger between Gulf banks in recent years at a time when several other banks are consolidating.
This is the latest in a number of potential merger activity across banks in the Gulf Arab as they seek to consolidate their position in an overbanked sector and contend with slower economic growth.
Earlier this month, Saudi British Bank secured a binding deal for its acquisition of the lender's smaller rival Alawwal Bank.
In Oman, Alizz Islamic Bank and Oman Arab Bank signed a memorandum of understanding for a potential merger.