Frenkel, 70, is currently the chairperson of JP Morgan Chase International, and his appointment came about despite the fact that Stanly Fischer, the current governor, recommended and supported Karnit Flug, Fisher's deputy governor, for the role.
He has been the target of criticism during the last few years because he served as the vice president for AIG while the company collapsed during the financial crisis towards the end of 2007.
Frenkel graduated from the Hebrew University's Economics Department and holds a Ph.D from the University of Chicago.
Between the years 1991-2000 he led the Bank of Israel and during his second term he tendered his resignation, claiming he "achieved all of the goals he set for himself."
He is famous for his policy of 'transverse exchange rate band' which created an apparatus for halting inflation. The policy was canceled in 2005 by Stanley Fischer.
After leaving his post in the Bank of Israel, Frenkel served as AIG's senior vice president; however he quit the post when the company nearly collapsed as a result of the US mortgage crisis.
The "too big to fall" company received $80 billion of a multi-billion dollar US stimulus package in an attempt to save it from going under.
Frenkel, like other senior AIG and bank officials who's respective companies were 'bailed out' with the help of taxpayers money, faced heavy criticism for their role in leading the market to the crisis, as well as the personal gains they registered both along the way and as a direct result of the crisis.
In his defense, during an interview to the BBC in February 2009, Frenkel claimed that it was impossible to foresee a crisis of such a magnitude and said that the bail out was intended to save the American economy, and not any specific company.
Prime Minister Benjamin Netanyahu on Sunday bid his farewell to the outgoing governor Stanley Fischer, saying "We've undergone a global crisis with stability to which Stanley greatly contributed."
"I would like to thank you for your important contribution to the Israeli economy as well as for your wit, perceptiveness and leadership, which have truly been a blessing to us all."
Frenkel's nomination will be brought for cabinet approval before finalized.