The British heavyweight champion could face a rematch with Wladimir Klitschko.
The fighter's mother is Nigerian and he reportedly tried to join the country's 2008 Olympic team.
Both Klitschko brothers have mingled with Trump during their boxing careers.
Fury says he needs to deal with his "medical treatment and recovery."
The self-confessed 'fat man' has gone on a health kick.
Fury is 12 years younger than Klitschko and three inches taller.
British boxer predicts an "easy win" against undefeated Ukrainian
Mayweather hopes to retire undefeated this year.