The Romanian sports channel Sport.ro have claimed that the Istanbul Giants have offered €5 million for the 25-year-old however, Tottenham are holding out for €7 million.
Sport.ro go onto state that Galatasaray have set aside €2.7 million per season in wages for the Romanian international.
Chiriches has fallen out of favour with Tottenham’s current manager Mauricio Pochettino following a string of disappointing performances.
Galatasaray have had a quiet transfer window compared to their cross-city rivals Fenerbahçe who have already made eight transfers this summer.
The Lions won the double a record sixth time last season and booked a place in the Champions League group stages for the fourth consecutive year.