Raum is wanted by Dortmund and the club have been working to sign the 24-year-old for several weeks.
A switch to Dortmund for the left-back is now becoming increasingly unlikely though, according to German daily Bild, with a host of Premier League clubs now keen.
Eddie Howe’s Newcastle and David Moyes’ West Ham are both interested in taking the Hoffenheim man to the Premier League.
It is suggested that both English clubs could comfortably meet Hoffenheim’s €40m asking price, while Dortmund, if they can reach the sum at all, would need player sales to do so.
The Ruhr giants’ best hope of snapping up Raum is now suggested to be convincing the player himself to make clear he wants to join Dortmund.
If Raum was to tell Hoffenheim he only wants to join Dortmund then the club’s position in the transfer chase would be strengthened.
Raum came through the ranks at Bavarian club Greuther Furth and was snapped up by Hoffenheim in 2021.
He has been capped nine times by Germany.