I didn't hear any new offer for Lautaro Martinez except the Saudi big deal which was refused by the player. I assume he wants to continue in Europe and probably in Inter for at least another season.
Otherwise Inter are looking for Aston Villa goalkeeper Emiliano Martinez. Until now they offered quite low price which was rejected by them, €15m...
Lautaro Martinez's decision that he still wants to stay in Europe is a pretty good thing for him because besides he still wants to make his career development in Europe, he might also still really want to play at Inter Milan with the aim of wanting to win in that team next season. Because I'm also pretty sure that Inter Milan will make it difficult for competitors in Serie A from the start of the season so they don't fall far behind as seen last season.