In a trading update, the firm revealed it expects to breach its banking covenants next month, while its debts for this year are expected to be between £875 million and £925 million.
Unite represents around 1,000 workers at the company and has has many more operating in its supply chain.
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The union's national officer for construction, Bernard McAulay, said: "Unite has hundreds of members at Carillion all of whom will be highly concerned about the company's financial situation.
"Aside from the directly employed workforce there are significantly more who are employed by sub-contractors and agencies on Carillion sites throughout the country.
"It is vital that the senior management of the Carillion Group sits down with Unite and provides a warts and all prognosis of the company's long-term future in order for our members to be properly informed of what the future holds. They need to know how Carillion intends to deal with its current financial crisis."
(LM/MH)
