Staff at Keelings' distribution facility in Ballymun, north Dublin, which delivers fruit and vegetables to Tesco, are threatening to take strike action.
Siptu began balloting its 375 members at the facility yesterday and voting is due to close at 3pm on Friday.
According to Siptu, the company has breached agreements on the percentage of agency staff to full-time employees employed in the factory.
This was set at 10 per cent but Pat Ward, a branch organiser with Siptu, said it is currently at 20 per cent or more.
The two sides are also in dispute about procedures for absenteeism and changes to the way security checks on staff entering and leaving the warehouse are conducted.
"Management is refusing to engage with us in any meaningful way," Mr Ward said. "If the strike goes ahead, supplies of chilled foods to Tesco may be affected."
Tesco is Ireland's biggest supermarket group with a 26 per cent share of the market. Mr Ward said staff had no issue with the multiple, its dispute was entirely with Keelings.
It is understood, however, that talks to avert a strike could take place later this month under the auspices of the Labour Relations Commission.
In a statement, Keelings said it was "disappointed" at the decision of staff to take a vote on industrial action.
"We are actively in talks with the unions to resolve the matter and are confident that these will facilitate a mutually-acceptable resolution," a statement from the company said.
Tesco declined to comment on the dispute. "This is a matter for Keelings," a spokesman said.
The Ballymun warehouse is one of five that supplies goods centrally to Tesco's network of more than 90 stores in the Republic. It has the capacity to handle up to 1.2 million cases a week. The facility is owned by Tesco but operated by Keelings' logistics arm, one of nine business units in the family-owned Keeling group.