According to Sunday's edition of Corriere dello Sport, the 28-year-old is set to make a 'sensational' return to the Italian club, after failing to hit the mark in England.
Anderson left Lazio for West Ham in 2018 in a deal that was worth around €40 million, and while his time in London started off well, it eventually faded and he was shipped out on loan to FC Porto last season, where he struggled massively.
The report claims that Anderson 'can really come back' to Lazio and that a transfer is 'possible' during this transfer window.
The deal is set to be an initial loan deal with an obligation to buy for €8 million, indicative of his drop in value over recent seasons.
With Anderson's contract expiring in 2022, the deal structure is set to be an €8 million transfer that will be completed in the coming year.
New Lazio manager Maurizio Sarri is reportedly a fan of Anderson, and he is looking to finalise a deal for the Brazilian as soon as possible.
The Serie A club's fanbase has been showcasing its desire for Anderson to return to the club, with him being a fan favourite prior to his move to West Ham, with him playing in 177 games for the Italian club, scoring 34 goals and providing 39 assists in all competitions.
The deal could be completed over the next few weeks, with West Ham keen to offload him and free up some funds for future signings.