Former Red Devils boss offered four-year contract by the Turkish club.
David Moyes has been offered the opportunity to manage Galatasaray, according to the Daily Mail.
Moyes, who was sacked by Manchester United in April, has travelled to Istanbul and is considering a four-year deal.
Galatasaray are currently managerless after parting company with former Manchester City boss Roberto Mancini earlier this month.
Moyes, 51, is apparently cautious about the prospect of working in Turkey, but an annual pay packet of £3.2m could convince him to give it a go.
Galatasaray finished second in the Turkish league last season, but they won the domestic cup and reached the last 16 of the Champions League.
They will compete in the Champions League again next term.
Moyes was only in charge of United for 10 months. He failed miserably in the Premier League, but he oversaw a decent run in Europe, before Bayern Munich defeated the Red Devils 4-2 on aggregate in the quarter-finals.