Gomez, 20, is a big fan of Aniston, who is known for playing role of Rachel Green for a decade in popular sitcom "Friends".
However, Gomez was completely starstruck by the actress, who has starred in movies like "Bruce Almighty", "Horrible Bosses" and "Wanderlust".
"I ran away from Jennifer Aniston. When she said, 'Hi', I was terrified of her. I was scared, so I ran away and I'm really embarrassed about that," Gomez said on a radio show.
"I didn't know what to do - it's Rachel," she added.