This would enable Delek shareholders to hold directly the shares of Delek Real Estate, a subsidiary of Delek Group.
"The company maintains sufficient retained earnings, should the decision be taken to take one of the above mentioned possibilities," Delek said in a statement.
Delek Group owns 79.9 percent of Delek Real Estate, whose shares have been battered in the wake of the global financial crisis.
Delek Group, which has interest in the real estate, energy, automotive and financial sectors, is 62 percent-controlled by billionaire Yitzhak Tshuva.