The club parted company with Roberto Mancini at the end of last season, despite finishing second in the Super Lig and winning the Turkish club under the guidance of the Italian.
The club are in the process of identifying his successor and granted Moyes an audience with Unal Aysal in Istanbul yesterday. The 51-year-old's future has been uncertain since he was sacked as manager of Manchester United in April - he was named as a candidate to replace Neil Lennon at Celtic - but it is understood that he is not yet convinced of a move to Turkey.
Reports yesterday suggested that the feeling may be mutual since a spokesperson for Galatasaray confirmed that the club would prefer to appoint either Joachim Loew or Juergen Klinsmann. However, with both coaches embroiled in the last 16 of the World Cup with Germany and the United States respectively, it is uncertain whether or not they would entertain an offer to succeed Mancini.
Moyes is not so encumbered and has intimated in the past that he is keen to coach abroad. Much could rest on his conversation with Aysal, though. "We are not in a rush, we are waiting for the end of the World Cup. The first two targets are Loew or Klinsmann," said a spokesperson for Galatasaray.
"The president has given a speech about it. 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."