Akanji has gained admirers for his performances in the Champions League this season, with the 22-year-old helping Basel progress to the last 16 of the competition.
Borussia Dortmund are allegedly keen to push through a deal in January but according to The Independent, Liverpool have entered the race for the Swiss international's signature.
The report suggests that Basel accept that the centre-back will leave the club in the near future, but it has been claimed that FCB would prefer to wait until the summer to sell to Liverpool.
Basel could also see Akanji's value rise before the start of next season, with the youngster likely to represent Switzerland at the World Cup.
Akanji has earned four caps for his country since making his debut in June.