Speaking at the club's AGM, Watzke said: "I would like us to get a complete picture of their opinions."
The three-year deal, announced in May which includes marketing, advertising and hospitality arrangements, and is reported to be worth 20 million euros ($19 million), has prompted criticism from Dortmund fans and further afield.
On Sunday, members spoke out against the sponsorship, with some having constructed mock tanks and an instruction stand with information about the deal.
In a non-binding vote on the first day of the AGM, 556 of 855 members on site voted against the deal, while 247 voted in favour, with 52 abstentions.
Watzke, who will sign off after a 20-year tenure running the club in 2025, said the result of the vote was a "clear signal" against the deal but said it was only a "first indication" given the small sample size.
"It is 0.25 percent of our members," the 65-year-old said.
Speaking on Sunday, Watzke defended the deal but said he "lost sleep" over it. "It was a tough decision which took a personal toll on me, but I stand by it," he added.
