The Italian midfielder stepped out on the Celtic Park turf for the first time since 2009 on Tuesday.
Hamilton face Mark Warburton's Glasgow Rangers at Ibrox next month.
A select round-up of the latest news involving Mark Warburton's Glasgow Rangers and Brendan Rodgers' Hoops.
Former Celtic midfielder Donati will reportedly train with Martin Canning's side this week.
The Italian midfielder left Parkhead seven years ago.
Leeds United sporting director Nicola Salerno has admitted that the club want to sign an experienced midfielder.