Negotiations have been ongoing for weeks, with Lazio reportedly holding out for around €50million.
However, with the add-ons offered this time looking easily achievable, it is thought that president Claudio Lotito would be inclined to accept the offer.
The bonues on offer are appearance based, and the player would be a regular should he make the move to east London.
It would give a significant boost to West Ham fans, who have been teased by players such as Javier Pastore in recent weeks, only to see them sign elsewhere.