The 22-year-old broke into Newcastle's first-team three years ago, but he has failed to cement his place in the club's starting XI.
Ameobi has shown sporadic signs of his talent and had a positive impact when he came off the bench in Saturday's 2-2 with Hull City in the Premier League.
That may be enough for the winger to start against Crystal Palace in the League Cup on Wednesday, but Newcastle manager Pardew has warned him that he must start living up to his potential or face an exit from St James' Park.
"Sammy is a player who has unbelievable talent and we have been waiting and waiting for him to deliver something on the football pitch," Pardew told reporters.
"I warned him last week that I am running out of time with him and he is running out of chances.
"Against Hull, he came on and changes the game a little bit, running up the pitch and taking players on.
"That is what we want from him but then he concedes a free-kick and we could lose the game. These are the things you have to learn even in a pressure situation like Saturday."
