The 25-year-old was close to joining Birmingham City during the transfer window but the move failed to materialise.
According to Goal's sources, Acquah will likely sign a three-year deal with an improved package next week.
"Birmingham really showed 100 per cent interest in Acquah. The president of Torino and Mihajlovic showed their belief in Acquah and decided not to make him leave," Arthur told Toro.
"The coach spoke to Acquah and assured him he has a place in his team for this season. It's true [that Acquah has been offered an improved contract]. The president has confirmed a renewal for Acquah. We would have discussions next week. Lots of the people are on vacation this week and the player was also with the national team.
"Even with the player's dream of playing one day in England, he is committed to Torino and ready to renew his contract," he added.