Slim's company already owned 27.4 percent of FCC but said its stake had increased to 36.6 percent after it bought into a 709.5-million-euro rights issue which ended last week, Reuters reported, citing a statement made by the company to the Madrid stock market regulator.
Under Spanish law, a shareholder that increases its stake in a company above 30 percent is required to launch an offer for the company.
FCC has struggled since Spain's housing bubble burst in 2008 and is heavily indebted although it managed to attract Carlos Slim and other investors looking to snap up Spanish assets with a view to a potential recovery in the country's real estate sector. Microsoft co-founder Bill Gates is one such investor, with a 3.92 percent stake in FCC, according to the latest filing.
Slim and Gates are not the only foreign investors interested in Spain. In 2014, hedge fund billionaires George Soros and John Paulson took major stakes in Spanish real estate investment trust Hispania but Soros decided against investing in FCC in 2014.
FCC was not immediately available for comment when contacted by CNBC.
Reuters contributed reporting to this story.
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