The England U19 international had been linked with a January exit from Selhurst Park and has not put pen to paper on new terms despite the fact it would significantly bump up his salary.
"Nathaniel has got a year-and-a-half to run and there's a lot of water to go under the bridge," Parish told the South London Press. "He could be on a lot more money than he is on, but he's thinking about that offer.
"We don't want these guys thinking about it every day - they need to concentrate on their football as well.
"I don't think it is a question that Nathaniel doesn't want to sign a contract - at this stage he wants to keep his options open and that's fine.
"That's the best thing to do in order to get a better contract or get the move he might want to the Premier League. We're all in a good place - me, his agent and the player."