Building materials firm CRH is in talks with Cemex to buy US and European assets from the Mexican cement maker.
The two firms said the deal was subject to due diligence, shareholder and regulatory approval.
"Depending on the scale of businesses included in any potential deal, and the outcome of due diligence, the total value of the transactions could range from $3.5 billion to $4.5 billion," the firms said.
CRH added separately that it had "sufficient balance sheet capacity to debt finance any transaction that might take place".
The assets include operations in Florida and Arizona that Cemex is obligated to divest by the US regulator as a result of its acquisition earlier this year of Australian building materials group Rinker Group.
The deal will also include other US interests, as well as businesses in Spain, Austria and Hungary.