The Portuguese club were reportedly denied in their first approach for the Italian player, who is believed to have several interested parties in his own country
The 23-year-old is widely expected to leave Torino in the summer after spending the last five years of his career at the Serie B side.
Obgonna, who was called up by Italy coach Cesare Prandelli last month, is reported to have garnered interest from both Juventus and AC Milan.
However, fresh speculation suggest Benfica, too, have expressed their intention to sign Ogbonna as they look for a replacement for Luisao.
The Brazil international has been at the Estadio da Luz for eight years now, but Paris Saint-Germain's interest could be enough to prompt an exit.
It is believed Torino have rejected Benfica's first offer of €12 million, as they look to receive at least €4m more for Ogbonna.