The 25-year-old scored eight goals in 34 appearances for Lazio last season, and according to the Mirror he is also attracting attention from the likes of Monaco and Valencia.
He looked set to join the Hammers last month but Lazio are rumoured to have upped their asking price, and thus there looks set to be a bidding war for the player's services.
West Ham fans also got excited by a photo posted on Anderson's Instagram which appeared to show the player on his way to Italy, with supporters speculating that he could be there to hand in a transfer request, or discuss his future with Lazio.
Anderson joined Lazio from Brazilian side Santos in 2013, and has since been a constant regular in the starting line-up, making 137 appearances in five seasons at the Rome based club. He has also made one appearance for the senior Brazil team, and has represented them at Under-20 and Under-23 levels.
While West Ham's interest in Anderson seems to be the strongest at the moment, it would not be a surprise to see Chelsea making a firm bid in the coming days.
The 2016-2017 champions were disappointing in the Premier League last season, finishing in fifth place and out of the all-important Champions League spots, and the club will certainly be looking at some fresh faces as they attempt to become title challengers once more in the forthcoming season.