The Serious Fraud Office (SFO) is looking at the company's former energy activities in Nigeria, as part of a broader corruption investigation that also includes Brazil, China and Indonesia, the business newspaper said without citing its source.
The SFO is examining whether Rolls and its agents were involved in any bribery of government officials until 2013 when tenders were launched for the building of energy infrastructure, the FT added.
"We are aware of the story but can neither confirm nor deny our interest in these specific allegations. Our investigation continues," an SFO spokesman said in an emailed statement.
"Concerns about bribery and corruption involving intermediaries in a number of overseas markets remain subject to examination by the SFO and other authorities," a company spokesman said.
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"We are co-operating with the authorities. We do not comment on the subject of ongoing investigations nor on the countries in which those investigations are being conducted.
"We have made it clear that Rolls-Royce will not tolerate business misconduct of any kind."
London-listed Rolls-Royce had meanwhile sold its energy production arm to Germany's Siemens in 2014 for 950 million euros.
"This is negative and an unfortunate development for Rolls-Royce, as the investigation is now understood to expand rather than shrink," said KeplerCheuvreux analyst Christophe Menard.
"In addition, it covers both the aerospace (in China and Indonesia) and energy (in Nigeria and Brazil) divisions, hinting at some potential past malpractices across the organisation."
He added: "Financial implications of the SFO investigation are unclear at this stage, but there is also reputational damage at play."
The troubled British company, which makes engine systems for aircraft and sea vessels, has been slashing costs after issuing a string of profit warnings over the last two years.