Palermo's attorney Robert J. Simandl asked Richard Saks, attorney for Voces de La Frontera, the immigrant rights group that has been representing the Palermo Workers Union, to "remove the barriers for a vote by our employees on a representation election."
Some Palermo workers have been on strike since June 1 because of alleged unfair working conditions at the company.
Palermo's has denied engaging in any unfair labor practices.
The National Labor Relations Board is reviewing the allegations against the company, which has delayed an election that was planned for July 27.
Irv Gottschalk, regional director of the NLRB, said a vote would include people who are currently working at Palermo's, striking workers and those terminated for immigration issues.
Each of the groups' votes could be challenged by the union or the company, and Gottschalk expects challenges because of disputes over employee statuses.
"There are just so many moving parts here it's hard to say this group yes, that group no," he said.
The investigation will continue for several more weeks, since the union on Thursday filed an amended charge alleging the temporary staffing agency that has helped Palermo's hire new workers, BG Staffing, is also terminating and threatening striking employees.
"We're certainly making progress," Gottschalk said. "The company's response is due next week and we'll see if that requires any follow-up."
Palermo's President Giacomo Fallucca also reached out to national AFL-CIO President Richard Trumka last week to discuss the labor dispute. The national union announced its support for Palermo Workers Union last week.
"There has been much misinformation communicated regarding Palermo's," Fallucca said. "Our company's mission to is deliver a great pizza experience, to its employees, its customers and its community. Since our founding, Palermo's has cared a great deal about our employees, and we believe it is important for our workers to have the opportunity for their voices to be heard. I am also hopeful that reaching out to labor leadership and asking for an open dialogue will help facilitate a better understanding of our position."