The 26-year-old defender will have a year left on his contract at the end of the season and he has been linked with a move away from Dortmund, with Manchester United and other Premier League sides keen.
Akanji rejected a contract offer worth €7m per year from Dortmund and he is expected to be on his way out of the club in the summer.
Manchester United are amongst the Premier League clubs who are interested in getting their hands on the Swiss defender ahead of next season.
But according to German magazine Kicker, Dortmund are still holding on to the hope of Akanji signing a new contract with the club.
Dortmund have already agreed on a pre-contract with Bayern Munich defender Niklas Sule for a move in the summer.
They are still pushing to convince Akanji to sign a new contract and stay on at Dortmund in the coming years.
However, the Bundesliga giants do not have the financial latitude to improve on their first offer by much for the defender.
Akanji is believed to be keen on a move to England in the summer if he does not sign a new Dortmund deal.
