According to a report in Haaretz, Zionist Union MK Tzipi Livni has been offered the post of UN Under-Secretary General.
Ms Livni reportedly met UN Secretary General Antonio Guterres several weeks ago to discuss the job.
Ms Livni’s office said she had not yet received an official offer, however.
Meanwhile, Mr Guterres sent a letter to all members of the UN Security Council last week saying he wanted to appoint former Palestinian Prime Minister Salam Fayyad as the UN's special envoy to Libya.