A report in the Daily Mail says it is a three-way race, with US computer games firms Midway and Electronic Arts (EA) amongst the suitors.
It is thought that private equity firm Apax Partners has also expressed an interest in SCi, which was worth £345.2m (€511m) before its statement this morning.
SCi said: “The board notes today’s press comment and confirms that it has received approaches from various parties which may or may not lead to an offer for the company.”
According to the newspaper report, Midway is the front-runner in the takeover race.
Midway – best known for the Mortal Kombat series of fighting games – is controlled by Viacom chairman Sumner Redstone through an 80 per cent stake in the publisher.
But it is dwarfed by EA which is the world’s largest computer games firm and publishes titles such as FIFA Soccer and Harry Potter and the Goblet of Fire. The company is listed on the New York Stock Exchange.
News of the bids come less than a month after SCi showed signs that its efforts to return Eidos to profitability within 12 months of ownership were working.
Operating profits of £1.6m (€2.4m) were achieved by Eidos in the seven weeks since Sci clinched a £74m (€109.5m) takeover in the middle of May – fuelled by strong sales of its Championship Manager game and distribution of Lego Star Wars.
SCi has offices and development studios in London, Bath and Derby as well as Europe and the US.
Because a bidder is likely to pay a premium for control, SCi chief executive Jane Cavanagh is in line for a substantial windfall from a takeover deal.
Ms Cavanagh, who founded SCi in 1988 and masterminded its stock market flotation eight years later, still owns 6.7 per cent of the firm. Her stake is worth £22.8m (€33.7m) at current prices.