Sources said talks between Goshawk and the Japanese Nikko Group regarding a possible takeover are set to resume this week.
Goshawk called off initial negotiations but Goshawk chairman Paul Spencer said he would be happy to re-enter negotiations with any parties who have "concrete proposals".
Nikko confirmed an initial approach had been made to the Goshawk board with regard to a "possible cash offer" by Nikko Group for Goshawk.
But it is understood that Goshawk ended the talks because, after six weeks, Nikko Group's UK private equity arm, Nikko Principal Investments, failed to come up with a figure it was prepared to pay for Goshawk .
A source close to Goshawk said that at that point the company had written to the board of Nikko to end negotiations because they were "going nowhere".
Goshawk's shares rose 10% on Nikko's announcement that it had made an approach to the insurer's management.
A Nikko spokesman said: "We have made a very serious approach which we think needs further discussion and we are doing what we can to ensure the approach is given further consideration."
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