They reports that 'Hammers' officials will meet their Lazio counterparts next week to discuss a deal for the 25-year-old, with Manuel Pellegrini understood to be a huge admirer of the player.
West Ham are expected to make an official bid of around €35m at that meeting, with the club hopeful that will be enough to get their man.
Anderson is exaclty the sort of nimble, tricky, pacey player Pellegrini wants to add to his squad and the Brazil international is thought to be open to a move to the capital.
Meanwhile, West Ham also remain hopeful of signing PSG star Javier Pastore, though that deal is currently being held up by the Argentine's wage demands.