The former Manchester United boss has held talks over succeeding Roberto Mancini but the Turkish club are keen to speak to Germany's Joachim Low and USA coach Jurgen Klinsmann
The 51-year-old was sacked just 10 months after he succeeded Sir Alex Ferguson at Old Trafford and has been without a club since April 22.
Galatasaray held initial discussions with Moyes on Friday but the Turkish club are prioritising moves for either Germany coach Joachim Low or USA boss Jurgen Klinsmann ahead of the Scot.
"The president has given a speech about it,” a Galatasaray spokesman told Press Association Sport.
"He said that we just spoke with David Moyes and he said that he can come to Galatasaray but he is not one of the main targets for us.
"They just spoke to each other, exchanging ideas - that it is it. It is true the president talked with David Moyes.
"We are not in a rush, we are waiting for the end of the World Cup. The first two targets are Low or Klinsmann."