Toffees boss looks to raise transfer funds through sale of South African
The South African, whose contract expires in the summer, has been constantly linked with a move away and Moyes has conceded the midfielder may be sold in January.
"We have had two offers and one of those offers has been accepted," said Moyes.
"We have allowed his representatives to speak to the other club, but whether it goes through or not, I don't know yet."
Chelsea were reported to have held talks with the winger, but Carlo Ancelotti has since dismissed any speculation that discussions were made between the two parties.
Pienaar is widely tipped for a move to the continent with a major European club with AC Milan being mentioned but Moyes would not be drawn on the speculation.
The midfielder has made a huge impact at Goodison Park following his £2 million switch from Borrussia Dortmund in 2007.
A new contract had been offered to Pienaar but Moyes revealed that he rejected the offer, which means the club could lose the player on a free in the summer and the Everton manager admits he felt resigned to losing 28 year-old since the summer.
"I think the player probably decided that [he was going to move] when he turned down his contract six months or a year ago, whenever it was," said Moyes.
"But he has done very well for us on the pitch, so we have no complaints."
Moyes claims he has no money to spend in the January transfer window so any transfer fee for the South African may come as a welcome bonus.
Everton have already seen a first-team member leave this month as striker Yakubu joined Championship side Leicester City on a loan deal until the end of the season.