The 25-year-old joined the Toffees from Standard Liege in 2008 for a club record fee of £15 million and has since established himself as a fan favourite at Goodison Park.
Felliani has scored eight goals in 15 games this season and been linked with a big money move away from Merseyside. However, Pienaar believes his Belgian team-mate will stay beyond the upcoming window.
"He’s enjoying his game at the moment so I don’t think he’ll want to disturb that progress," Pienaar told the Liverpool Echo. "He’s clever enough not to go.
"I don’t think he will go in January. I’m sure the manager will keep hold of him.
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"There’s a lot of speculation about but he’s still contracted to the club, and if we keep going like this we know it might still be hard to keep hold of him in the future – but who knows? He’s been very important to us the last few weeks."
However, the South Africa international stopped short of saying his Belgian team-mate would never call time on his spell at Goodison, and stated that he would not criticise Fellaini if he chose to move.
Pienaar continued: "He’s a grown man and everyone makes his own decisions. You have to make decisions that have risks in life.
"If you’re scared to get out of bed and take a risk, you’re not enjoying life. I think if the opportunity comes for him eventually and he takes it we’ll wish him all the best but I definitely don’t think it’ll be in January."