Eurosport cites sources claiming that the Turkish Super Lig giants are looking to the Scot as a prime contender for the vacant position at their helm:
The Huffington Post's Samuel Luckhurst supports these claims with images of Moyes in Istanbul, while the Daily Mail's Matt Lawton illustrates just how close he is to re-entering the management world:
The Telegraph also has information on the meeting, tweeting the following:
Galatasaray are currently without a manager following Roberto Mancini's departure from the club by mutual consent, as reported by Sky Sports earlier this month.
Moyes was axed from his role as United boss after 10 months in charge at Old Trafford, failing to live up to his tag as "The Chosen One," but Paul Handler of the Manchester Evening News says that offers have been rife.
Galatasaray have a firm bond with British managers, as Luckhurst points out:
Handler quotes Moyes after he spoke on his employment prospects earlier in June, where he gave an idea of just what he's expecting his new project to offer:
I have had a couple of opportunities to go back in and chosen to do do anything just now. I am going to look for what I feel is the right opportunity. I got my real first taste of the Champions League this year and I thought I showed I can manage at that level. I would like somewhere that would give me a chance of being in the Champions League or a club that has ambitions of being in the Champions League.
It could be at home or abroad. I have always liked the thought of broadening my horizons and learning a bit more and at the moment I am quite comfortable watching and learning. I will go away and learn and look again to see what is happening.
Europe was at times the one consistently bright spot in Manchester United's dismal 2013-14 season under Moyes, where they went unbeaten throughout their Champions League group campaign and pulled off a remarkable comeback in their round of 16 tie opposite Olympiakos.
The journey eventually came to its end at the hands of then reigning champions Bayern Munich, but not before United held a good account of their talents in a 1-1 first-leg draw.
Moyes' time at Old Trafford has become the butt of many a joke, but one could argue that the odds were so firmly stacked against him that few managers might have fared better under the same circumstances.
A move to Turkey would give the 51-year-old a very enticing prospect in a club that has ample resources and the chance to deliver in the European forum once again.
Gala finished second to Fenerbahce in the Turkish top flight last season and will be hoping to rise back to the summit following Mancini's exit.