The row comes in the wake of tensions between Israel and the European Union over new guidelines that bar EU funding for any Israeli entity operating in the occupied Palestinian territories.
Talks with Bucharest on importing Romanian manual labor broke down in 2012, the radio said, but resumed at Israel's initiative after a new Romanian government came to power in May of that year.
Differences center on Bucharest's request that Israel guarantee no Romanian construction workers would be employed on the settlements, which are considered illegal under international law.
The Romanian foreign ministry confirmed to AFP that the talks were continuing and said Bucharest's position would be consistent with "respect for international law, the positions of the EU and the protection of Romanian citizens."
It said the latest draft of the accord had been sent to Israel in August for possible revisions, adding that "the negotiations are nearing the end."
It was Israel's second diplomatic row with an EU country this week following a dispute with the Netherlands over a new security scanner to be installed on the Israel-Gaza border that Dutch Prime Minister Mark Rutte was to have inaugurated Sunday.
The Dutch government had hoped the scanner would serve to facilitate an increase in the export of goods from Gaza to the West Bank, while Israeli officials accused the Dutch of trying to impose "political conditions."
Also on Sunday, Dutch Foreign Minister Frans Timmermans refused to accept an Israeli military escort around Palestinian-ruled areas of the West Bank city of Hebron.
The European Union guidelines, which go into effect in January, ban funding for and financial dealing with projects linked to settlements in the West Bank and annexed East Jerusalem.
All Israeli settlements are illegal under international law.
Israel has announced thousands of settler homes since peace negotiations began in July.