The first petition to hit the High Court was adjourned for two weeks yesterday.
The action was brought by recruitment firm MCR Personnel, trading as the MCR group, which claims it is owed €1.793 million by Elliott.
MCR is demanding the cash for recruitment services provided over a six year period.
The Irish Times said MCR was seeking to have P Elliott put into liquidation on the grounds it is insolvent and unable to pay its debts.
The court was told the contractor is facing other winding up petitions from a number of trade creditors with one of those petitions due to be heard by the High Court next week.
William Cox Ireland and Oran Precast have lodged petitions seeking to have the firm wound up while subcontractor OMC Engineering has served a 21 day notice on the company seeking payment of €100,000 due for work carried out on a number of projects.
Elliott drafted in accountant Ernst & Young last month when most of its staff across Ireland were let go.
The 2012 contract is the firm’s largest job in the UK where it has also picked up work with supermarket chain Lidl in London and moved to a new office in Canary Wharf in February.
Elliott started on site in December 2009 on the £30m contract to build plot N14 of the Athletes Village which is due for completion in August. Up to 280 people are employed on the site.
An Olympic Delivery Authority spokesperson said: “Following discussions with P Elliott, a way forward has been agreed by both parties to ensure that the work on one of the 11 residential plots in the Olympic Village will be completed.
“Construction work across the wider Olympic Village site is firmly on track.”