According to Football Italia, Torino are hoping to include Acquah as part of an exchange deal for Stoke City midfielder Giannelli Imbula.
Imbula has failed to make his mark in the English top tier since his arrival from Porto and he is reportedly keen on moving to the Serie A.
Stoke Sentinel further suggests that Stoke and are in advanced negotiations with the 25-year-old Black Stars midfielder.
Acquah has also been linked with a move to Newcastle United where he would team up with fellow Ghanaian international Christian Atsu.
Since moving from Ghanaian Premier League side Bechem United, the midfielder has spent almost his entire European career playing in Italy where he has also featured for Palermo, Parma and Sampdoria.
He also had a spell with Hoffenheim in the Bundesliga.
Should the move to the Potters materialise, Acquah will be joining Atsu, Andre and Jordan Ayew, Daniel Amartey and Jeffrey Schlupp who are all playing in the English Premier League.