The Tottenham playmaker, who may cost in the region of £5million, impressed in a six-month loan spell with the Toffees last term.
Pienaar made his name with Everton in the 2009/10 campaign, scooping the side's player of the season accolade before joining Spurs in January 2011 in pursuit of Champions League football.
However, injuries and intense midfield competition at White Hart Lane prompted his temporary return to Merseyside, with a permanent switch appearing imminent.
"I think we are much closer to Pienaar and hopefully in time I will have something, but I don't quite have it yet," Everton manager David Moyes said on Saturday.