The Hammers remain locked in talks with the Serie A club over a deal for the Brazilian as Manuel Pellegrini, alongside newly appointed director of football Mario Husillos, looks to add quality to the ranks ahead of the new season.
The east Londoners have already signed Ryan Fredericks on a free transfer, while they are also closing in on deals for Swansea goalkeeper Lukas Fabianski and Toulouse defender Issa Diop.
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Anderson, 25, missed the early parts of last season through injury but was a mainstay in the Lazio midfield as they finished 5th in Serie A and reached the quarter-finals of the Europa League.
That European experience will be key in Pellegrini’s interest as the Chilean targets a continental spot in his time at London Stadium.
Anderson, who has previously been linked with Southampton, has one cap for Brazil and has not been included in their squad for the World Cup in Russia this summer.