The 20-year-old forward is expected to move on from Red Bull Salzburg in the summer with several big clubs chasing him.
He is one of the talents Liverpool have been tracking with a view to potentially signing him in the next transfer window.
But Adeyemi has been heavily linked with a move to Dortmund and the forward is believed to have agreed personal terms on a contract.
And according to German daily Bild, the Bundesliga giants are even ready to put in more money to sign the striker in the summer.
They were initially prepared to offer around €35m and are now ready to add a few more million to their bid.
It has been claimed that Dortmund are now ready to go up to €38m in order to snare Adeyemi away from Red Bull Salzburg.
But that is still short of what the Austrian giants want, which is believed to be around the €45m mark.
Dortmund are keen to play a waiting game as they are certain that Adeyemi only wants to join them in the summer.
