The meeting, at the London offices of East Midlands' advisers, Schroders, was called on Monday at the request of Dominion. The talks are understood to be between East Midlands chief executive Norman Askew, its finance director, Bob Davies, and Dominion chairman Thomas Capps and chief financial officer Linwood Robertson.
They followed Dominion's announcement last week that it was considering a bid at a price not much in excess of 608p a share, giving East Midlands a minimum valuation of pounds 1.2bn.
Nottingham-based East Midlands scoffed at the price, saying it undervalued the company's prospects.
Speculation that Dominion might be prepared to come up with an increased offer pushed shares in East Midlands higher yesterday. They closed at 611p, up 7.5p on the day, after touching 618.5p in earlier exchanges.