The 29-year-old, who turned out 90 times for the Parkhead side, is said to be keen on a move to America, and a short-term deal with the Easter Road side could benefit both the club and the player.
McCourt, who played briefly under Hibs manager Pat Fenlon at Derry City, is a free agent following his Parkhead exit.
Capped 13 times for Northern Ireland, McCourt scored 16 goals during his time at Celtic, and according to his brother, it is ‘99 per cent nailed on’ that the winger will go to America.
Leroy McCourt told the BBC: “He’s just been in [at Hibs] today to have a look around and do a bit of training.
“It’s really just to keep his fitness up. It’s always been the intention to go to America.”
The MLS season comes to an end at the end of October, and the player’s brother added: “He doesn’t want to uproot his family at this stage of the season over there.”
McCourt recently spent time training with Peterborough, with manager Darren Ferguson saying in July that he hadn’t given up hope of signing the winger.