Precinct Investment last night said the €1.30 per share offer for the hotel group had received acceptances from shareholders holding 37% of the company's shares.
Precinct is seeking 54% support to take control of Gresham and will up the offer to €1.35 per share if 80% of shareholders accept the bid.
Precinct is owned by a trio of businessmen Bryan Cullen, JJ Murphy and David Coleman who have circled the company for some months.
The stumbling block to the takeover going ahead is the 28% stake held by Red Sea Hotels, the Israeli company that took control of the board two years ago. Its shareholding and that of the Indian businessman Chanrai Balrau, who owns 11% of the company, is currently being investigated by the Irish Takeover Panel.
It is inquiring whether the two shareholders are acting in concert. If the panel finds they are, Red Sea and Mr Balrau would be forced to mount a full takeover offer themselves. Under Irish company law, if any shareholder goes above 29.9% they are required to make a bid at the highest price paid for the shares. This would mean Red Sea and Mr Balrau would be forced to make a higher offer of €1.34 per share.
The takeover panel is expected to begin its hearings into Red Sea and Mr Balrau this week. The move by the Takeover Panel followed complaints from Gresham and Precinct.