U.S. health insurer Anthem Inc (ANTM.N) said on Saturday it had offered $46 billion in cash and stock for smaller rival Cigna Corp (CI.N) but that a deal was being held up in part over what role Cigna CEO David Cordani would have in a merged company. Anthem, the second largest health insurer in the United States, said that it had made four offers for Cigna in June, sweetening each one with a bigger total offer or an increased cash component for a premium of 35.4 percent.