The Ghanian international, who has made 19 Serie A appearances for Juve this season, will be available on a free with his Bianconeri contract set to expire in the next week.
According to previous reports, AC Milan were hoping to convince Asamoah to join Gennaro Gattuso's side. However, it now appears that I Nerazzurri have won the race for the 29-year-old's signature, and he is expected to sign a three year deal worth €3.5m a year, after he completes his medical on Wednesday.
Asamoah joined Juventus from Udinese in 2012 and has made a total of 115 appearances for the club since. He's struggled to establish himself in Massimiliano Allegri's side this year, however, and reportedly rejected a new contract offer in January.
A number of Premier League clubs were linked with a move for the defender, including Chelsea, West Ham and Everton.
Inter are currently three points behind fourth-placed Lazio in the league table. The two sides are set to meet on Sunday in the final game of the season at the Stadio Olimpico, and I Nerazzurri will need to beat the hosts by at least four goals in order to qualify for the Champions League.
Even if they do fail to qualify, Luciano Spalletti will want to strengthen the squad with Europa League qualification already guaranteed, and the arrival of Asamoah is expected to be closely followed by the arrival of Lautaro Martinez, who is set to sign from Argentine side Racing de Avellaneda.