Sky Sports says the Potters have agreed a £15million fee with Galatasaray for Ndiaye.
Arrangements are now being made for the Senegal star to fly to England for a medical and to discuss personal terms.
Talks are still ongoing about the exact structure of payments. Legal matters are also to be resolved.
And the move has been somewhat complicated by the need for a visa to enter the UK.
Only once that has been granted can Stoke then apply for a work permit.
Stoke will not fork out any cash until they are sure Ndiaye will be granted international clearance.