The Merseyside club announced they had given the 28-year-old permission to speak to Spurs, who had an initial offer turned down last week.
Pienaar, who is out of contract at the end of the season, would now seem to have a choice between Spurs and London rivals Chelsea, who have already had a bid accepted by Everton.
An article on Everton's website read: "Everton can confirm they have agreed terms with Tottenham over the possible transfer of Steven Pienaar."
Source: PA
Source: PA