Talks for ex-Southampton player Ramirez, 29, were held on Monday and progressed very well.
However, Ramirez has yet to give his ‘ok’ to the move and has other offers on the table.
The Uruguay international has spent the past three seasons at Sampdoria, scoring 16 goals for the club.
Torino have also contacted Bournemouth in an ambitious attempt to sign Josh King.
And while Torino know it will be difficult to bring him to Italy, they plan to make a big effort.
Bournemouth, who were relegated from the Premier League last season, have yet to receive any official offers for King.
This could help Torino who are able to offer the Norwegian forward regular football in Serie A.
Torino lost their first two games of the new season, scoring just two goals. Signing both King and Ramirez would add more potency and creativity to their attack.