Under an agreement between the bank and IDB, first refusal rights will expire if there is no deal by November 11.
The $100 million fund will invest in early stage insurtech startups.
The bank is believed to be considering the sale, in view of the recent rise in Clal Insurance's share price.
Non-banking companies will be able raise up to NIS 20 billion.
The beta trial of the Israeli company's app will begin in the coming weeks,
Kobrinsky is likely to continue outgoing chairperson Joseph Bachar's backing for CEO Lilach Asher-Topilsky.
The former Phoenix chairman will be supervisor of the Capital Market, Insurance, and Savings Authority.
Israel Money Laundering head Adv. Shlomit Wagman-Ratner tells "Globes" that money is becoming more and more difficult to hide.