Goretzka is out of contract at the Veltins Arena in June and has been linked with a host of leading European clubs, including Liverpool, Barcelona and Juventus, but Marca and Sport Bild claim Bayern have stolen a march on their rivals and struck a deal with the 22-year-old.
Schalke's sporting director Christian Heidel insisted on Monday that nothing had yet been agreed and Heynckes was giving little away as he prepared to fly to Qatar with Bayern for a warm weather training camp.
"You'll have to wait and see," he told reporters.
"If I read it correctly, his manager [Jorg] Neubauer said that they have not yet decided. The Spaniards are still there in the race."
Heynckes is happy for the player to decide on his next career move, adding: "He is a bright, intelligent boy. He knows exactly what is best for himself."
Goretzka has helped Schalke to the lofty heights of second in the Bundesliga with four goals in 11 appearances this season on the back of a superb showing in Germany's Confederations Cup triumph, although a stress fracture in his lower leg has interrupted his progress of late.
Table-topping Bayern resume Bundesliga action at Bayer Leverkusen on January 12.
"It's a very short [break], so you have to use the time smartly - the intensity of the training [must] pick up where we left off," said Heynckes.