Two major insurance companies are on the market. Billionaire Yitzhak Tshuva's Delek Group chose to keep its energy assets over Phoenix Holdings. Argentinian businessman Eduardo Elsztain, who now controls IDB, the former vehicle of convicted tycoon Dankner, is looking to sell Clal Insurance .

Neither have been able to finalize a deal, both saying stepped up regulation scared away investors.

"It's funny to be in a process that we have to sell in three years, but nobody can achieve that," Elsztain said.

IDB appointed JPMorgan to find a buyer for its 55 percent stake in Clal following two failed attempts to sell to Chinese investors. Under an agreement with the regulator it may have to sell off 5 percent of the company every four months.

"A forced sale will make a tremendous loss to shareholders," Elsztain said at a news conference.

Two weeks ago, businessman Zadik Bino sold a small fraction of his 23 percent stake in refiner Paz Oil for 8.2 million shekels to an unnamed financial body.

His lawyer David Hodak confirmed to Reuters it was a "symbolic" first sale and that Bino as of now planned to reduce his stake in Paz to below 5 percent so he could keep his holdings in the First International Bank of Israel.

Hodak also headed a government committee in 2010 that created new parameters for how institutional investors could operate in the debt market after the global crisis.

He argues that government interference has since gotten out of hand.

"Foreign investors look at what happened to Israel and are seeing many changes, over-regulation," he said. "Yes, we have opportunities but I don't think that we create appetite for foreign investors."