The Roman outfit are keen to acquire the services of the Turkey international, who has also been linked with Borussia Dortmund and Atletico Madrid.
Lazio sporting director Igli Tare said on his club's official website: "Lazio is doing everything it can with regards to Trabzonspor and the player.
"We still need time to complete Yilmaz's negotiation.
"It's a long and delicate negotiation and we must be patient."
The 26-year-old Yilmaz set a new club record by scoring 33 league goals in 34 appearances last season for Trabzonspor.
Yilmaz is under contract with the Super Lig side until June 2015.