Reports claim that the player has failed to agree terms to a move to England after travelling from Germany, despite the Bundesliga side being happy to sanction a deal.
Durm, who struggled with injuries at the Westfalen Stadium, did not make a single Bundesliga appearance last season.
Town are batting with Fulham to sign Leicester City striker Ahmed Musa, according to reports.
The Nigeria international - impressive in the World Cup - joined the Foxes from CSKA Moscow in the summer of 2016, for a fee believed to be worth in the region of £16.6m, but he has failed to establish himself at the King Power Stadium.
Leeds United have been linked with a move for Chelsea midfielder Lewis Baker.
The 23-year-old is likely to leave Stamford Bridge again, with the player having a difficult loan spell at Middlesbrough last term and previously hitting the heights with Vitesse Arnhem.
Middlesbrough have been linked with Newcastle United’s £15m-rated winger Matt Ritchie, who is wanted by Stoke City.
Rotherham United are close to signing free agent and central defender Clark Robertson, 24, Blackpool’s player of the year last season.