The Romanian is seemingly set to exit White Hart Lane after failing to convince since his 2013 arrival.
The 25-year old Romania international joined from Steaua Bucharest two summers ago for £8.5 million - according to the Express - but has struggled to settle in England.
Tottenham’s summer business thus far has further reduced his chances of making an impact next season, with centre-backs Toby Alderweireld and Kevin Wimmer joining from Atletico Madrid and FC Koln, respectively.
Galatasaray’s offer represents a £5 million pound loss for Spurs and Daniel Levy, and their rejection of the bid comes as no surprise.
At 25-years old, Chiriches is approaching his prime and is still captain of his national side, who this week entered the FIFA rankings top ten.
He has shown glimpses of his quality during his time at Spurs but has never really adapted to the pace of the Premier League. There is reason to believe, however, that his style of play could be suited to a league played at a slower tempo, and Serie A outfit Roma have been linked with a move in the past by Sky Sports.
Levy is known for his skills as a negotiator and he will need to call upon all of that expertise if Spurs are to get a fee close to what they paid for the enigmatic Romanian.