Pienaar has ignored massively improved terms from Everton and is free to negotiate a deal with foreign clubs from January.
Moyes admits: "In my head I've resigned myself that he'll probably be leaving at the end of the season.
"But we'd love him to stay and if he wants to stay we'll be here for him at any time. He's in the last year of his contract so we'll just have to let it go and see how it ends up.
"But I've also said I'm happy with what we've had from him. He cost us £2.5m and people in the last year of their contract tend to play out of their skin because they're trying to impress suitors.
"If it's money they want they're going to have to play well for people to say they're worth the money they want. So I'll try and use the situation to my advantage this year and get the best out of him I can. But I have to say he's been playing well."
Moyes also said that Pienaar had promised him his commitment will not dip despite his failure to sign a new deal.
Moyes added: "When he spoke to me about it, he said 'boss, whatever happens I'll do my best in all the games and you'll never find me wanting.'
"He's admitted the club is good for him.
"At the moment I've got to say he's been standing up and doing some really good things on the pitch.
"Maybe he wants Champions League football and I'd love to be able to give that to him and I think he'd be able to help me get it. But maybe those are his ambitions. I hope we can still talk him round and Steven will say Everton have been really good for him in his career.
"But Steven's turned it round, not Everton. He's the one that's done it, but I hope that if there was any doubt in his mind he will stay.
"As we know the grass isn't always greener. There's a really good contract offer for him there if he wants it."