The striker is currently on a salary of €2.7m, while Mundo Deportivo says Barca have tabled a contract worth €7.5m-a-year for five seasons.
Inter are demanding €90m plus one player from Barca for an overall value of €111m - Lautaro's buyout clause. Barca's latest proposal is for €70m cash and one unnamed player.
But while terms are important, the biggest pull for Lautaro is the prospect of playing with Lionel Messi at Barca.
Lautaro also wants to be regularly challenging and winning trophies - something he feels he has a better chance of achieving with the Blaugrana.