Rovers are keen to find a replacement for Michael Weyman, who retired earlier in March due to injury.
Canberra coach Ricky Stuart has left Shillington out of his team for the first two rounds of the NRL this year.
Instead, Shillington has played two games for the Mount Pritchard Mounties in the New South Wales Cup.
He is currently sidelined for two months with a broken thumb sustained playing for the Mounties.
The 31-year-old is one of Canberra’s highest paid players. There is interest in him from Australia, too, with Gold Coast and Manly said to be keeping tabs on him.