Fifa's deputy secretary general Jerome Champagne confirmed to BBC Sport that Blatter will meet Ayacko on 20 July and said the pair are likely to be joined by Kipchoge Keino.
They are bound to Formula One by the "Concorde Agreement" until the end of 2007 but would be free to set up a new series in 2008 should the sport's chiefs not meet their financial demands.
FILA, the sport's international governing body, will meet in Moscow on Saturday to discuss major changes designed to improve wrestling's standing with the IOC.