The 23-year-old, whose brother Sam has returned to the Rabbitohs after a spell in rugby union, said in May that he was keen to play in the NFL.
Jarryd Hayne, another National Rugby League player, left Parramatta Eels to join the San Francisco 49ers this year.
It is understood the Giants hold weekly trials, and that Burgess was one of many to take part on Thursday.
Burgess, born in Dewsbury, West Yorkshire, began his career at Super League side Bradford Bulls, but only spent two seasons there before moving to NRL club Rabbitohs where he joined his brother Sam and twin George.
The England international was part of the Rabbitohs side that beat St Helens 39-0 to win the 2015 World Club Challenge.
South Sydney Rabbitohs prop Tom Burgess has had a trial with the New York Giants American football team.