Mittal, main shareholder in steelmaker ArcelorMittal as well as being chairman and chief executive, was keen to secure larger supplies of iron ore, said the newspaper.
Rio, one of the world's major producers, is the subject of a contested bid by Australian mining group BHP Billiton, worth about $160 billion at present share prices. The deal is being scrutinised by anti-trust regulators.
The Financial Times said Mittal's thinking emerged as his adviser Goldman Sachs announced he had joined the board of the Wall Street bank.
"Mr Mittal has considered some involvement in the takeover, such as the idea of taking a stake in Rio through buying from existing shareholders," it quoted an unnamed banker as saying.
"On the other hand, he could wait until later, when quite possibly some of the iron ore assets (of Rio) go on sale as a result of demands by anti-trust regulators," said the banker.
The Financial Times said bankers believed Rio's iron ore assets were currently worth about $50 billion. But this figure could fall sharply in the next few months, particularly if the boom in steelmaking starts to peter out.
No immediate comment was available from ArcelorMittal on the report.