It reported revenues of more than £5bn in 2016, and is one of the largest construction service multinationals in the UK.
Her views were echoed by Unite union assistant general secretary Gail Cartmail, who said: "The government must consider all options while the future of Carillion hangs in the balance, including bringing contracts back in-house".
A government spokeswoman said: "Carillion is a major supplier to the government with a number of long-term contracts".
Scottish Labour's shadow economy secretary Jackie Baillie called on the Scottish Government to clarify the potential impact if Carillion collapses.
Carillion has a pension deficit of roughly £580m, although this figure would be expected to rise sharply if measured according to the cost of insuring its various retirement schemes on a full buyout basis.
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Mrs May faced calls to be more courageous in bringing about change and diversity to refresh the look of the government . He promised to talk about trade, immigration, Britain's European Union exit costs, and the transition deal.
"If the government is forced to institute a rescue package they need to also ensure that the supply chain is fully protected".
The Wolverhampton-based group is the second-largest supplier to Network Rail and maintains approximately half of the UK's prisons as well as roughly 50,000 homes for the Ministry of Defence.
In addition to its rail operations, Carillion also manages almost 900 schools, provides services to the NHS and works with National Grid.
Carillion, which has had to contend with a slowdown in many of its major markets, has seen its share price plummet from 230p a year ago to less than 15p on Friday.
The company is seeking financial support from commercial lenders or the government to avoid being put into administration.
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She explained that she and Kanye could have gone through the process anonymously but that she wanted to make sure that the woman they chose was 'a fan'.
"You can see that one the one hand, it's in everybody's best interest that Carillion continues, but at the same time it's hard to chart a way forward".
The meeting comes as Carillion - a major government contractor on projects including High Speed 2 - races to secure additional funding to avoid collapse, with around 19,500 United Kingdom jobs at risk. It also has contracts in many other industrial sectors.
Carillion met ministers from a wide range of government departments on Thursday to discuss contingency plans for the company's collapse.
A spokeswoman said: "It is too early to predict the outcome of these discussions but Carillion expects that any such agreement is likely to involve the raising of new capital and the conversion of existing financial indebtedness to equity which would result in significant dilution to existing shareholders".
It said the firm remained in constructive dialogue about short-term financing while "longer term discussions are continuing".
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We have a good relationship with Theo, and I don't want him to be frustrated or lose an opportunity to go the World Cup. He said: "We'll see". "If that can be sorted out it would be a great addition from an attacking point of view".
Last month, Carillion said it received all necessary consents to defer the test date for both its financial covenants from December 31 to April 30, 2018, and that it was continuing constructive talks with stakeholders on options for cutting net debt and recapitalizing.