The 28-year-old South African international is out of contract at the end of the season and has been linked with a move to Chelsea and Spurs.
Moyes said: "We have had two offers and one of those 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."
Reports have also suggested that Pienaar could have already signed a pre-contract agreement with a major European club.
Chelsea boss Carlo Ancelotti was tight-lipped over any potential move for Pienaar when asked at a press conference ahead of his team's home match with Blackburn on Saturday.
There are a lot of rumours, a lot of speculation and names," said the Italian. "Maybe sometimes some agents are using the names to earn more money.
"Pienaar is a good player and we know him very well, but this doesn't mean we need to have him play here. We are thinking about central defence.But if we find the right player for us, we have the possibility to buy."Pienaar joined Everton for £2m from Borussia Dortmund in 2007 and was voted the club's player of the season last term.But his form this season has not been at the same level and Moyes revealed that the player rejected a new contract some time ago.Everton will be keen to recoup a fee for the player rather than watch him leave for free at the end of the season.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."If Pienaar makes a transfer window move he would be the second player to leave the club in January.On Thursday striker Ayegbeni Yakubu joined Leicester on loan with a view to a permanent deal.