The 25-year-old right-winger scored four goals and provided seven assists in 21 appearances in Serie A last season.
He also scored three goals in seven appearances in the Europa League as Lazio made the quarter-finals, where they were beaten by RB Salzburg.
Anderson has been one of Lazio’s stand-out players for several seasons, having signed from Santos for £6.75m in 2013, and has been of interest to English clubs in the past.
He won a cap for Brazil in 2015 during an excellent campaign but lost form during the 2016-17 season.
In 177 appearances across five seasons for Lazio, Anderson has scored 34 goals and provided 42 assists.
West Ham are actively trying to do business before the World Cup begins in Russia following the arrival of Manuel Pellegrini as their new manager.
The Hammers are in talks to sign Genoa defender Armando Izzo and Fulham right-back Ryan Fredericks, while they are also interested in Barcelona’s Marlon Santos and West Brom’s Jay Rodriguez, according to Sky sources.
Manchester United, meanwhile are interested in signing West Ham forward Marko Arnautovic, according to Sky sources.