Moyes has been chasing England target man Crouch for a month after finding out who could be available as Harry Redknapp wheels and deals to get the men he wants.
Now the clubs are in advance talks about brokering a move that would see South African midfielder Pienaar go to Spurs - with the size of fees being discussed and decided.
Tall order: Everton want to use Steven Pienaar (right) in a swap deal for Tottenham striker Peter Crouch
Redknapp likes Pienaar and his chief scout Ian Bloomfield watched him at the weekend. He has gone to the top of his wish list because West Ham will not part with Scott Parker and Stephen Ireland chose Aston Villa ahead of them.
Moyes wanted to keep Pienaar, but he will consider trading him for the right fee in this window as he would be a free next summer - and virtually worthless in January.
The Goodison boss is desperate for a new striker as Louis Saha has failed to fire, Yakubu is still on West Ham's list and new boy Jermaine Beckford is being asked to be the number one after joining on a free from Leeds.
In the Red: Crouch history with Liverpool may prove to be a barrier in his relationship with Everton fans
Moyes is a big admirer of Crouch and thinks he would bring a new dimension to his side. The fact that he played for Liverpool does not put him off.
Crouch is aware of Everton's interest and has his doubts about the move. However he also knows that Redknapp could be leaving him out of the Spurs team when he has his other strikers fit.
The tall striker's wages will also be an issue for Everton solve, but he could be paid off by Spurs in his part of the deal to keep him within the Goodison pay structure.
The move is described as 'close' by insiders although Redknapp would have to land a striker to make up for Crouch's absence.
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