The 28 year-old starred for the Turkish side last season in the league and also in the European Champions League but now wants a bigger challenge.
In a meeting between himself and also coach Faith Terim, it is believed that he has asked for a transfer elsewhere meaning that he wanted to play in a higher league.
Lazio who have long been after his signature have struck personal terms with a 5 year contract and an annual salary of 2.5 million euros being mooted.
There has been a suggested transfer fee of 3 million euros for an initial loan then another 9 million euros to make a permanent move but the offer has already been laughed off by Galatasaray president Unal Aysal.
Yilmaz has been a prolific goal scorer for the Turkish Super League champions with 34 goals and 9 assists from no more than 47 appearances last season.