The player's talks broke down with Chelsea on Friday after they had a £3m bid accepted by Everton last week.
Tottenham are reluctant to increase their bid with the midfielder out of contract in the summer.
Chelsea talks: Pienaar (left)
Spurs boss Harry Redknapp is bemused by the deal, saying: 'I can'tget to the bottom of it. I think I do know but I'll end up in bigtrouble.
'It's very strange to me how they have suddenly offered £3m. The manager at Chelsea, who is a lovely guy, comes on TV and he denies it. I don't think he is a liar.'
Toffees manager David Moyes expects Pienaar to be at training this morning.
'He will be in training because at the moment we don't have a deal,' said Moyes. 'If Tottenham offer the same money that may change or maybe he will agree 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.'
Pienaar was left out of the squad for Sunday's 2-2 draw in the 215th Merseyside derby after telling Moyes he did not want to play.
'Steven came to see me on Saturday and said he didn't feel he was in the right place to play,' said Moyes, who is keen on Burnley's Chris Eagles as a replacement.
'I had a decision to make and I felt it would be better not to use him if that was the case.'
All square: Moyes watched his Everton side share the points with Liverpool
His side did well enough to prove there is life after Pienaar, recovering from Raul Meireles' opener to score twice in the first six minutes of the second half through Sylvain Distin and Jermaine Beckford.
Moyes was denied his first Anfield victory in nine attempts by Dirk Kuyt's 68th-minute penalty.
'I am disappointed we didn't take all three points after the second half but delighted to only come in 1-0 down after the first half because Liverpool were the better team,' said the Scot.
'In the first half we never got to the pitch of the game and it looked as if we had some young players in the team who looked overawed by the start of the game.
'Liverpool won all the duels so it needed a word to correct it at half-time and in the second half we were terrific.
'I thought we had a chance when it went to 2-1 because we were on top but we were missing three or four big players.
'I know Liverpool were missing two (Steven Gerrard and Jamie Carragher) but it is different for a club like Everton, who have a much smaller squad.'
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Explore more:People: Harry Redknapp, Jamie Carragher, Sylvain Distin, David Moyes, Dirk Kuyt, Steven Gerrard Places: Liverpool