Zaha was the subject of a failed transfer bid by Arsenal earlier this summer.
The Gunners could not meet Crystal Palace’s financial demands and have instead opted for Nicolas Pepe from Lille.
It has left Zaha seeking a move elsewhere with it clear he no longer sees his future at Selhurst Park.
READ MORE: Why Zaha was Arsenal’s top target
The Toffees are ready to test Palace’s resolve with a bid in the region of £50m.
Tottenham, meanwhile, are not currently in the position, nor do they want, to make a similar move.
They are aware of Zaha’s availability but are currently pursuing other targets.
Mauricio Pochettino is looking to lure his compatriot Giovani Lo Celso to north London.
He is also keeping tabs on Paulo Dybala’s availability at Juventus with a move away being touted.
But any swoop for Zaha would mean Tottenham smashing their transfer record for the second time in this window.
Palace are doing all they can do keep the Ivorian having already seen Aaron Wan-Bissaka swap London for Manchester in a £50m deal.
The transfer window is also nearing its closure meaning the Eagles would have little to no time to seek a replacement should Zaha move on.
He has previously expressed a desire to play Champions League football which is why he may favour a move to Tottenham over Everton.
Pochettino’s side pipped Arsenal to fourth place in May and reached the Champions League final.