Hanover International is understood to have asked its financial adviser NM Rothschild to seek a buyer prepared to pay more than the surprise £38.2m, 125p-a-share offer made last week by Trefick.
Trefick, the investment vehicle of entrepreneur Jack Petchey, made the mandatory offer last week after boosting its stake in Hanover from just over 29% to 49.15% in a day.
The Hanover board said the bid significantly undervalued the chain of 12 four-star hotels and three conference and training centres, which has a net asset value of 200p per share. It added that it was "pursuing all options to realise greater value for shareholders".
Trefick's offer documents are expected soon, and the Hanover board will then have two weeks to respond.
However, it is also understood that the Takeover Panel is looking into how Petchey increased his stake so rapidly, to ensure he did not breach takeover regulations.