Sacked Old Trafford boss could replace former Man City manager Roberto Mancini in Istanbul.
Galatasaray are in talks with ex Manchester United and Everton manager David Moyes, according to the Daily Mail.
Moyes was sacked by United in April, ending a disastrous 10-month reign at Old Trafford.
He is said to be keen on a swift return to the game – something that Galatasaray are offering him.
Galatasaray parted company with Roberto Mancini earlier this month after failing to win the Turkish league last season.
Moyes has been identified as a top target by Galatasaray and the club have apparently offered him a four-year contract worth £3.2m per year.
The 51-year-old Scot is reportedly cautious about working in Turkey, but he is willing to discuss the role, having flown out to the country today.
Galatasaray will compete in next season’s Champions League – a competition that Moyes fared reasonably well in with United.
Moyes guided the Red Devils, who finished seventh in the Premier League, to the quarter-finals of Europe’s top club tournament.
United were eliminated by a 4-2 aggregate defeat to Bayern Munich, after holding the German champions to a creditable 1-1 draw in the first leg in England.