The Italian side are reportedly keen on a loan deal for the Ecuadorian striker.
West Ham's Enner Valencia
The Ecuadorian striker could depart the Hammers this summer, especially if they secure the new striker they are desperate to sign.
Liverpool's Jon Flanagan in action with West Ham's Enner Valencia
Talks are already underway to take him to Italy and it appears that a deal could be struck before too long.
According to La Repubblica, talks are progressing well between the two clubs, with West Ham accepting a paid loan to with a view to a permanent deal.
They have only accepted the outline of a deal though, with the finer details still needing to be ironed out.
West Ham's Enner Valencia in action with Norwich City's Timm Klose
Lazio want to pay £2 million initially with a further £9.4 million later, but West Ham are hoping for a future fee of £11 million instead, according to the report.
It now remains to be seen if a deal can be struck, although this latest report suggests that an agreement is close to being agreed before too long.
Valencia scored four goals and created 12 chances in 19 Premier League appearances for West Ham last season.
Enner Valencia celebrates scoring for West Ham