The Turkey international left the Bundesliga giants in 2011 for Real Madrid but was unable to break into the first team and was loaned out to Liverpool in the summer of 2012.
However, Sahin also failed to find his feet at Anfield, and a move back to Signal Iduna Park was paved through thanks to interest from all those involved.
"I think we're all aware that the salary structure here is different from Real Madrid's," Zorc told Bundesliga.com.
"However, Nuri accepted what we offered as for him it was all about wearing Borussia Dortmund's shirt again. There wouldn't have been a chance to sign him otherwise."
Zorc has refuted claims that Dortmund brought Sahin back in a bid to keep on equal terms with Bayern Munich, and he insists that the player has the quality to make the 18-month loan from Santiago Bernabeu a success.
"Sporting matters always come first, no question," the club chief continued.
"Nuri hasn't enjoyed much playing time in the last 18 months, but we're all aware of his qualities, which is why we're convinced he'll be a great asset in the coming years.
"I'm sure he'll be able to link up very well with all our midfielders and his footballing ability is outstanding.
"Our guiding principle was doing what we felt was best and most useful to Borussia Dortmund. This transfer has nothing to do with Bayern."