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 has been reported on Friday that 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, who will be available on a free transfer in the summer, will sign a pre-contract agreement with a major European club.
Moyes did not comment on those reports at his weekly press conference 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."
Source: PA
Source: PA