Lazzari has struggled to fit into Maurizio Sarri's style of play, and could be set to leave Lazio in the upcoming transfer window.
Lazio are open to selling him in January, putting a €15 million price tag on the Italian.
According to Tuttosport (via InsideFutbol), Torino are set to make the first move to sign him, with them set to enter negotiations with Lazio over Lazzari in the coming days.
Torino are set to propose a player plus money deal, with them keen to allow Zaza to join Lazio, with him only playing a bit part role for Torino in Serie A this season, both because of injuries and of underwhelming performances.
In contrast, Sarri is a huge admirer of the 30-year-old striker, and with Vedat Muriqi reportedly set to leave the club, Lazio are in need of a striker to rotate Ciro Immobile with.
It is still unknown whether Lazio will be interested in such a deal, and if the likes of Spurs or Bologna will offer more money or submit a better offer overall, but right now, Torino seem to be leading the race.
Lazzari has regularly featured for the Biancocelesti this season, but mainly out of his natural position at right-back instead of higher up the pitch, while Zaza is yet to score a goal for Torino this season.