The Rome club have reportedly agreed a deal for the former Fenerbahce striker, and will beat off competition from the likes of Borussia Dortmund for his signature
According to reports in Corriere dello Sport, the Biancocelesti chief is expected to fly out to Turkey to finalise a deal after authorising the payment of an initial €5 million for the 26-year-old, with another €1.8m to follow in October.
Newly-appointed coach Vladimir Petkovic is said to be a keen admirer of Burak, who scored 33 goals in 33 appearances for his club in the Super Lig last season.
With the terms of a contract already agreed with the player, the Rome club are confident that the Turkey international will boost their striking options ahead of the new Serie A season.
If the deal goes ahead, Lazio will have beaten Borussia Dortmund and a number of English Premier League clubs to Burak's signature.