Galatasaray are looking for a new head coach after parting company with former Manchester City boss Roberto Mancini at the end of last season.
Moyes was sacked by United in April and his next move has been the subject of considerable speculation.
Galatasaray have confirmed reports that the Scot has been in Istanbul to meet with president Unal Aysal, but described the talks as merely an exchange of ideas and said that Joachim Low and Jurgen Klinsmann are their top targets.
A Galatasaray spokesman said: "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.
"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."
Low is currently in charge of the Germany side at the World Cup in Brazil, where Klinsmann has also impressed in charge of the United States.
The implication that Moyes would be interested in a move to Galatasaray supports the belief the 51-year-old may return to work overseas. He has previously been linked with jobs in Germany.
Moyes began his managerial career with Preston before spending 11 years at the helm at Everton.
His relative success at Goodison Park attracted him to United when Sir Alex Ferguson retired last year but his reign at Old Trafford lasted just 10 months.
United, champions in 2013, slumped to seventh in the Barclays Premier League last season and failed to qualify for the Champions League.
Galatasaray, who finished second in their domestic league and won the Turkish Cup under Mancini, have previously been managed by a Scot in Graeme Souness.
Souness spent a year in charge of the Istanbul club from 1995-96 and earned infamy when he planted a Galatasaray flag in the centre circle at the ground of arch-rivals Fenerbahce.