A group of employees at an Apple store in Maryland started a drive to form a union on Tuesday, the Washington Post reported.
Organisers at the Towson Mall store near Baltimore said they had signatures from more than 65 percent of employees who are likely to be eligible, according to the report.
The union intends to file paperwork with the National Labour 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.
In other news, Amazon workers voted against unionising a second warehouse in New York City, a ballot count on Monday showed, representing a defeat for labour organizers who just weeks ago secured their first US win at the retailing giant.
Sixty-two percent of workers at the Staten Island facility opposed the union push, with 618 employees voting no and 380 in support, according to results released Monday by US officials.
The election at the LDJ5 warehouse followed on the heels of an upset April 1 win by the Amazon Labor Union (ALU) at the much larger JFK8 Staten Island company site — which established the first American union at the retail colossus.
Last month's win stood as one of the biggest recent victories by US organised labour, winning plaudits from US President Joe Biden and other leading unions, some of which visited Staten Island ahead of the second vote.
But the ALU acknowledged its latest setback at Amazon — the second biggest private employer in the United States after Walmart.
"The count has finished. The election has concluded without the union being recognized," the ALU said on Twitter. "The organizing will continue at this facility and beyond. The fight has just begun."
Backers of the union drive said Amazon was well prepared for the latest vote and had aggressively campaigned to quash momentum from the earlier victory.
Further complicating their efforts, union leaders were not as well-known as at JFK8, where the ALU's president Christian Smalls had previously worked.
Smalls launched the drive after being fired in March 2020 for organizing a protest for personal protective equipment during New York's first major Covid-19 outbreak.
"At the end of the day, this is a marathon not a sprint," Smalls told reporters. "We all know there are going to be wins and losses, we're going to fight another day."