The Merseyside club have, though, turned down Tottenham's offer for the midfielder.
Moyes revealed the South Africa midfielder was left outof the squad for Anfield after telling him that he did not want to be involved.
Where to now? Everton midfielder Pienaar is wanted by a host of big clubs at home and abroad - but Chelsea look set to win the race for his signature
The Scot said after Sunday's 2-2 draw with Liverpool: 'We have accepted an offer from Chelsea. Steven has not agreed terms with Chelsea.
'We've given his representatives a chance to talk to Chelsea but they've not got permission to talk to Tottenham because they've not offered the same money.'
'Steven came to see me yesterday and said he didn't feel he was in the right place to play," added Moyes.
'I had a decision to make and I felt it would be better not to use him if that was the case.
'He will be in training tomorrow (Monday) because at the moment we don't have a deal.'
Pienaar, who will be available on a free transfer in the summer, has been on the radar of Europe's top clubs since signalling his intent to leave Everton.
Moyes said on Friday: '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.'
Pienaar has made a big impact at Everton since signing for £2million from Borussia Dortmund in 2007.
Blow: Pienaar's exit will leave a big hole in the Everton team for Goodison Park manager Moyes to fill
He was the club's player of the season last year but the Merseysiders have been unable to tie him to a new contract.
Talks with Pienaar had stalled but Moyes admitted that a contract offer was rejected some time ago, making his departure inevitable.
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 forus on the pitch, so we have no complaints.'
Pienaar's form this season has not matched that of previous years but heremains an important member of Moyes' side.
The club hope they can now recoup a fee for him rather than seeing him run down his contract.Moyes might appreciate the money having said he has no money to buy players this month and that any new recruits will be loan signings.
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