Tottenham, Manchester United and the Toffees' Merseyside neighbours Liverpool have been linked with the South Africa international, as he has just one year remaining on his current deal.
Pienaar has not ruled out the possibility of staying at Everton, who expect to secure Jack Rodwell on a new four-year contract on Monday, but he will not be prepared to accept a cut-price offer.
"I'd say the spirit of the discussions was very good, but we have differing valuations, so my future isn't clear," said the 28-year-old in the Daily Mail.
"Everton may keep me for the last year of my deal. If they decide to sell, and the move is correct for my career, then I'll consider it.
"Hopefully this hasn't been my last season, but who knows?".