The England international only signed a new long-term contract over the summer, but the club are keen to reward him for his consistent displays.
Arsenal were reportedly keen to land the ex-Sheffield United defender over the summer and Moyes wants to make sure he keeps ons of his star players at Goodison Park.
"He has got on with the job no problem and there will be a new contract offer for Jags later in the year," said Moyes.
"I've tried to keep my key players here and Jags accepted it, he was great about things."
However, one player who seemed increasingly likely to leave is South Africa international Pienaar, who is out of contract in the summer.
The skilful midfielder can depart for free at the end of the season and Moyes is losing hope that the parties can agree fresh terms.
He added: "We'd love Pienaar to stay, but I'm growing resigned to him leaving."