Like Gillespie, Obertan moved to Newcastle from Manchester United.
Gillespie told the Evening Chronicle: "I think he can be a real hit with the fans at Newcastle. Yes, he is a player that is going to be unpredictable at times. But he's certainly got the talent. He wouldn't have been at Man United if he didn't have that.
"It always takes a little bit of time to bed in. But I'm sure the fans will take to him by the end."