Zakaria is out of contract at the end of the season and is expected to leave Borussia Monchengladbach on a free transfer in the summer.
Gladbach have not given up on the prospect of the Swiss signing a new contract but he is expected to move on from the club as he looks for a new challenge.
Liverpool have been consistently linked with Zakaria, though according to German outlet Fussball Transfers, Arsenal have also joined the race, having spoken to his camp.
But it appears Dortmund have the edge in the race to sign him and, according to Sky Deutschland, the club have had positive talks with the player over a move to the Westfalenstadion.
The negotiations between the club and player’s representatives have been moving along smoothly.
It has been claimed that there is already agreement on some major issues between the player and Dortmund.
With no sign of him penning a new deal, Gladbach have not ruled out selling him in the January transfer window.
It remains to be seen whether Dortmund will make a move in January or wait until the summer to sign him on a free transfer.