According to Sky Sport Italia, the latest proposal is €30m guaranteed plus another €5m in relatively easy-to-achieve bonuses.
That is an improvement from the previous €28m plus €5m add-ons.
However, the same report from transfer expert Gianluca Di Marzio claims that Sassuolo are already going to reject it and stick to their guns.
The asking price for the Italy international remains €35m minimum, plus another €5m in add-ons.
They sold Gianluca Scamacca to West Ham United for €36m plus €6m bonuses and a 10 per cent cut of the sell-on fee, so believe Raspadori should go for a similar sum.
Unlike Scamacca, Raspadori was part of the Italy squad that won EURO 2020.
The 22-year-old scored 10 goals with six assists in 36 Serie A appearances for Sassuolo last season and has also been heavily linked with Juventus, but made it clear his priority is Napoli.