The 25-year-old joined Lazio in 2013 from Santos, and has been one of the key players for the club since.
Wanted by Manchester United and Chelsea in the past, Anderson has been one of the outstanding performers in the Serie A in recent years.
Known for his fine technical abilities, and his eye for creating chances for others, he would be a fantastic signing for any Premier League club.
According to the Daily Mail, the Hammers have launched an ambitious £35 million plus bid to sign the Lazio winger. Talks are underway at the moment with the player’s representatives are Anderson is eager to play for Manuel Pellegrini.
Anderson scored four goals and provided seven assists in 21 appearances in Serie A last season. He also scored three goals in the Europa League campaign.
The Hammers are also looking to sign Brazilian defender Marlon Santos. They have already lodged an offer of £13 million, and the defender is likely to join the Hammers in the coming days.