According to Fabrizio Romano of Calciomercato.com, the Old Lady have been eyeing the Switzerland youth international since he impressed at the 2014 UEFA European Under-17 Championship in Malta, but they could face competition for his signature as Real Madrid are also said to be interested.
Oberlin said during the Malta tournament he dreamed of playing for Juve in Serie A, while he also stated he would be eager to join Manchester United, per Calciomercato.
The 20-year-old is on loan at Basel from Red Bull Salzburg and has enjoyed an excellent start to the 2017-18 season.
He has netted five goals in a combined 10 appearances in the Swiss Super League and UEFA Champions League, including a double in Basel's impressive 5-0 thrashing of Benfica.
Per BT Sport Football, he scored again in Europe against CSKA Moscow on Wednesday and could have had more had he not wasted some fine opportunities:
His finishing needs work, but he has many of the attributes required to become a top-class attacker, including blistering pace and impressive ball control.
Able to play as a central striker or on the left flank, Oberlin could be a fine addition at the Allianz Stadium.
Juventus manager Massimiliano Allegri has overseen the development of a number of young attacking talents during his time at the club, including Alvaro Morata and Paulo Dybala.
If Oberlin continues to perform at a high level throughout the season, especially in the Champions League, Juve could come knocking for him next summer.