Manager David Moyes has now given the South Africa international, who is out of contract at the end of the season, permission to discuss a potential move in the current transfer window.
It was reported the 28-year-old has already held talks with Barclays Premier League champions Chelsea but those negotiations have broken down. It has also been claimed that Pienaar will sign a pre-contract agreement with a major European club. Moyes did not comment on those reports at his weekly press conference on Friday, but did confirm Pienaar could soon be leaving Goodison Park.
Moyes said: "We have had two offers and one of those offers has been accepted.
"We have allowed his representatives to speak to the other club, but whether it goes through or not I don't know yet."
Pienaar has made a big impact at Everton since signing for £2million from Borussia Dortmund in 2007.
He was the club's player of the season last year but the Merseysiders have been unable to tie him to a new contract.
It had been suspected that talks with Pienaar had stalled but Moyes admitted that a contract offer was rejected some time ago, making his departure inevitable.
When asked if Pienaar had decided he wanted to move on, Moyes said: "I think the player probably decided that when he turned down his contract six months or a year ago, whenever it was.
"But he has done very well for us on the pitch, so we have no complaints."
Source: PA
Source: PA