Lawyers for a group of protestors say their clients may be willing to give certain undertakings not to interfere with the work of Greyhound Recycling.
The waste management company took the protestors to court after bin lorries were allegedly blocked in an ongoing dispute over pay and conditions.
The dispute began in mid-June when workers went on strike over pay and conditions.
They claim the waste management company has effectively locked them out of their jobs in an attempt to force through a 35% wage cut.
The company denies this and has urged them to accept a Labour Court recommendation that would still see them earn more than the average rate.
Last week, People Before Profit Councillor Gino Kenny was ordered to stop engaging in what the High Court ruled to be "unlawful picketing".
The court also heard of incidents where lorries were blocked at various locations across Dublin city and that drivers were threatened and intimidated
Today, the company is pursuing further injunctions against People Before Profit TD Joan Collins, two other local councillors and a group of striking workers.
Lawyers for the politicians claim there may not be a need for such an order as they are willing to give certain undertakings.
The hearing is due to take at least two hours.