The Blues landed their man for a whopping €64 million (£57m/$73m) at the start of January before loaning him back to Dortmund for the rest of the season as part of the deal.
However, it was the player's decision to move to Stamford Bridge instead of one of their rivals, with Zorc confirming that matching bids from other clubs were received.
"I have to say that there was at least one more club that would have been willing to pay a sum on this scale," Zorc told Ruhr Nachrichten.
"The deal gives Chelsea security now and they do not have to enter a bidding contest in the summer, they have clarity and can plan with the player."
Whoever the losing suitors were, they will undoubtedly be disappointed to have missed out on a talented player with an enviable combination of youth and experience, having made 115 appearances for the Bundesliga leaders despite being just 20 years old.
Following the imminent departure of Pulisic, Zorc was asked about the club's plans to replace him.
The American has been on the fringes this season since the emergence of Jadon Sancho, being used predominantly as a substitute, but the sporting director confirmed that a replacement would be needed amidst links to Borussia Monchengladbach's €42m-rated (£37m/$48m) Thorgan Hazard.
"It's clear that Christian is leaving a gap, which needs to be closed by the summer," he added.
Dortmund currently top the Bundesliga and hold a six-point gap over reigning champions Bayern Munich, but face a tricky-looking trip to face RB Leipzig on Saturday when domestic action resumes following the winter break.