There are reports that Hyundai would sell Israel the vessels, and that various Israeli defense industries would install locally-made systems on board, including radar and Barak anti-missile system.
Some of the work could be done by the Israel Shipyards in the city of Haifa, located about 90 kilometers (56 miles) north of Tel Aviv.
Israel has voiced enthusiasm in purchasing four frigates from South Korea and plans to send a team of its officials to Seoul next month to pursue a potential deal.
"Israel recently expressed an interest to buy four frigates," Yonhap news agency quoted an official at South Korean’s state-run weapons procurement agency, Defense Acquisition Program Administration (DAPA), as saying Saturday on condition of anonymity.
The 1,400-ton frigates under negotiation with Israel are said to be priced at about US$100 million each.
South Korea offered to build warships for the Israeli navy after it lost a bid to sell Israel T-50 fighter trainer jets earlier this year.
A team of representatives from the South Korean government and Hyundai Shipyards visited Tel Aviv in April to discuss a deal aimed at building frigates for the Israeli navy.