Galatasaray's sporting director Bulent Tulun is in Rome to discuss the potential transfer of the 28-year-old and says an offer of £15.4 million will be accepted by the club
Burak, 28, is a highly sought-after striker following a prolific season in Turkey and in the Champions League where he scored eight goals in nine games last season.
The club's sporting director, Bulent, insists Burak will only go for the right price.
"If we get a good offer we can let Burak Yılmaz go," he told reporters.
The Turkish champions are reportedly demanding a fee of €18 million [£15.4m] for the attacker, but so far the highest bid they are understood to have received from Lazio has been €9.5m [£8.1m] plus bonuses.
Burak joined Galatasaray in July 2012 for €5m [£4.3m], and scored 32 goals in 39 appearances in his first season at the club. He previously had spells with Trabzonspor, Fenerbahce and Besiktas.
At international level he has appeared 27 times, finding the net on nine occasions since his debut in 2006.