If the Nottingham-based group is swallowed up, it would leave just four regional electricity companies (Recs) still independent, out of the original 12 at privatisation.
The most likely candidate to launch a bid for the company is thought to be the US utility firm, Houston Industries, which was previously linked to speculation about a possible approach for London Electricity.
Nigel Hawkins, a utilities analyst with Yamaichi International, said: "The window of opportunity to take over a REC is narrowing, given the imminence of a general election and the likelihood of a Labour government with a more hostile attitude towards utility takeovers."
Rumours of a possible bid for East Midlands boosted the share price last week to 580p, a gain of 30p. Yesterday a spokeswoman for East Midlands said: "We can only say what we always say, that we don't comment on speculation. As far as we're concerned it's business as usual."
With 2.2 million customers, East Midlands is one of the largest electricity companies by customer numbers. It is also widely considered to be one of the best-managed under chairman Nigel Rudd and chief executive Norman Askew.
Over the past two years they have steered the company away from activities such as retailing and security, concentrating on improving the efficiency of the core electricity operation. The total workforce has fallen to 5,000, from 8,700 in 1993. The management has also been sceptical of the potential savings from the "multi-utility" groups.
However, because of its efficiency, East Midlands would not come cheap. A buyer would have to offer at least 650p, a 70p premium over Friday's closing share price. Tough negotiating by the existing management could push the final price to 700p, valuing the company at pounds 1.4bn.
It is thought that if the two sides cannot agree a price this week, it could lead to a hostile bid. One analyst said: "If anyone is going to drive a hard bargain it's Nigel Rudd. He has more experience of takeovers than the rest of the management of the entire electricity industry put together."