HITC Sport understands that the Hammers want to make sure they secure a permanent deal.
The Argentine attacker joined the Hammers on a season-long loan deal in the summer from UAE outfit Al Jazira, who had snapped up the 22-year-old the year before.
West Ham were able to strike a deal worth around £10million with a £1m initial loan fee being paid.
Lanzini, who has an Italian passport, has become an important member of Slaven Bilic's side, starting six games so far this term and scoring some crucial goals.
Lanzini's appearances have, though, caught the eye of a number of clubs around Europe and especially elsewhere in the Premier League.
And now West Ham will make move to make sure they are not gazumped, and will soon open talks with Al Jazira to finalise the details of a deal which now looks very good business.