Thurston, who kicked the golden point field goal that saw the Cowboys beat Brisbane in one of the most memorable grand finals in years, is aiming to become the first man to win the award three times having been crowned the world's best player in 2011 and 2013.
Kiwi fullback Tuivasa-Sheck, who will join up with the Warriors for the 2016 season had a sensational final season with the Roosters, who claimed a third successive minor premiership.
Leeds and England fullback Zak Hardaker has also been named on a three-man short-list for the award after helping the Rhinos win the Super League grand final agains Wigan.