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Shareholders have been offered €1.38 (£1.26) per share, almost 16 per cent higher than the last closing price of €1.20.
US investor JC Flowers has a 25 per cent stake in HRE and has said he will not accept an offer below €3 a share.
"There is still a clear preference to remain a shareholder and thus to be treated exactly the same as other shareholders that had to go under [Germany's bank] rescue shield," commented a spokesman for Mr Flowers.
Earlier this week, German president Horst Koehler signed a bill backed by the government allowing the state to seize control of HRE as a last resort.
If the nationalisation goes ahead, it would be the first time the German government has taken the step since the 1930s.
