The 30-year-old has scored 116 goals in 167 appearances for the Biancocelesti, making him Serie A’s top scorer.
Immobile, who first made a name for himself at Torino, is under contract with Lazio until 2023.
However, his excellent form has led to rumours that Manchester United and other important clubs could go for him.
Lazio want to keep their goal-hungry forward in Rome and according to Tuttosport have a new contract ready.
The new deal would see Immobile sign a two-year extension until 2025 and earn an improved €4m-a-season salary.
Immobile could make himself an immortal at Lazio by becoming the club’s all-time top scorer.
The Italian international is currently fourth on 116 goals, only five behind Giorgio Chinaglia, 11 behind Giuseppe Signori and 43 behind the legendary Silvio Piola.
With an average of 29 goals per year, Immobile could soon break Piola’s record, which has stood since 1943.