The South Africa midfielder, who isout of contract at the end of the season, would have preferred a moveto White Hart Lane but the Merseysiders' desperation for funds toreinvest in the transfer market will force a straight cash deal to theleague champions.
Spurs have been leading the chasefor Pienaar for most of the season but Chelsea's surprise slump in formhas made Carlo Ancelotti look for a quick fix.
Ancelotti hopes to sign a defendertoo, after letting Ricardo Carvalho go last summer and losing Alex tothe injury list. Chelsea will sanction the spending on Pienaar, fearingthey could slip out of the Champions League places.
Losing out to their rivals will be ablow for Tottenham, and manager Harry Redknapp may have to consolehimself with FC Twente striker Bryan Ruiz, whose 24 goals helped SteveMcClaren's former side to the Dutch title last season.
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
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: '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.
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.
Blow: Pienaar's exit will leave a big hole in the Everton team for Goodison Park manager Moyes to fill
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.
Striker Yakubu became the first high-profile player to move this month, joining Leicester on loan on Thursday with a view toa permanentdeal.
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