The well-informed Phil Hay of The Athletic reports that Leeds are on the verge of agreeing a £13m (€14.5m) fee for Koch.
Newcastle are specifically mentioned and ‘at least’ one other English club are said to be in the race.
However, Italian side Lazio are not in the running for Koch, their sporting director has confirmed.
“There are currently no discussions [for Koch],” Lazio sporting director Igli Tare told Kicker on Friday.
Koch will report for national team duty with Germany on Monday.