Generali said a majority of non-executive directors had expressed appreciation for Donnet's work at a meeting on Tuesday and had welcomed his willingness to be re-appointed when the insurer names a new board in the spring.
Two people close to the matter said eight out of 12 board members at the meeting were in favour of Donnet.
Generali said the outgoing board would put forward Donnet as CEO if it decided to file its own slate of nominees - as it is allowed to do for the first time after a change in the company's by-laws last year.
Donnet's reappointment has been challenged by two leading Generali investors, construction magnate Francesco Gaetano Caltagirone and eyewear billionaire Leonardo Del Vecchio.
Caltagirone and Del Vecchio, respectively Generali's No.2 and No.3 investor, are ready to support an alternative CEO candidate, sources have said, while Donnet has the backing of Generali's single biggest shareholder Mediobanca.
Caltagirone and Del Vecchio are also investors in Mediobanca, Italy's leading investment bank.
In a sign that simmering tensions are coming to a head, Del Vecchio and Caltagirone on Saturday unveiled a consultation pact over their combined 11% Generali stake.
(Reporting by Gianluca Semeraro and Claudia Cristoferi; editing by Valentina Za)