The Rome outfit are looking to improve on the eighth-placed finish they managed in Serie A last year.
And according to Italian newspaper Il Messaggero, they believe strengthening their central defence is the key.
Chambers earned rave reviews while on loan at relegated Fulham from Arsenal last season.
Although he struggled when he played a defender and looked much more at ease in a holding midfield role.
The 24-year-old still has three years left on his Emirates deal after extending his contract last summer.
But the report claims that Lazio believe a £12.5m bid would be enough to persuade the financially struggling Gunners to sell.
With Aaron Ramsey departed for Juventus, Chambers would likely back himself to get game-time under Unai Emery next season should he stay.
Lazio are also eyeing up Newcastle captain Jamaal Lascelles according to the same report.
The 25-year-old is held in high regard by Magpies boss Rafa Benitez, but the club are in a state of disarray behind the scenes.
Whether Newcastle would consider cashing in on Lascelles remains to be seen.
But if they were to, the Tynesiders would surely demand more than the £12.5m that Lazio boss Simone Inzaghi is reportedly prepared to pay.
Fans of the St. James’ Park outfit have laughed of the price tag, claiming the sum should be at least doubled.
One supporter wrote: “Nowhere near enough, didn’t Michael Keane go for about £25-30m?”
“They might want to save a tree and not bother sending a fax if they intend on it reading €16m…” added another.
“Chump change,” a third fan tweeted.
“Double it at least!!” said a fourth annoyed Geordie.