Birmingham City boss Harry Redknapp, who is hoping to bolster his midfield ahead of the new campaign, was unable to sign Acquah's Black Stars teammate Emmanuel Agyemang Badu, who opted for Turkish side Bursaspor in a season-long loan from Italian club Udinese.
Acquah made 20 Serie A appearances and scored two goals for Torino last season.
He is expected to arrive in England within the week to undergo a medical and hopefully complete the switch.
Former Ghana U20 star Godfred Donsah of Bologna could replace Acquah if Birmingham’s move turns out successful.
Acquah boasts of 29 caps and one goal with Ghana since making his debut in 2012.