
Organisers at the Towson Mall store near Baltimore said they had signatures from more than 65% of employees who are likely to be eligible, according to the report.
The union intends to file paperwork with the National Labor Relations Board in the coming days, the Washington Post said.
Apple did not immediately respond to a Reuters request for comment.
Workers at an Apple store in Atlanta in April filed a petition to hold a union election, seeking to become the company’s first US store to unionise amid a wave of labour activity at other major firms.
Amazon.com workers voted against unionising a second warehouse in New York City, a ballot count on Monday showed, representing a defeat for labour organisers who just weeks ago secured their first US win at the retailing giant.