Bain Capital’s proposal would have valued the British company at 939.4 million pounds ($1.27 billion) on Wednesday.
Craneware’s shares were up marginally at 20.10 pounds at 0723 GMT.
Bain Capital separately said it would not make an offer for Craneware.
The proposed bid represented a 29.3% premium over Craneware’s closing share price on May 15, the day before Bain Capital disclosed its interest.
Craneware, which specialises in healthcare financial software for the US market, currently has a market capitalization of about 710 million pounds, according to LSEG data.
Discover the stories of your interest
The company’s shares had previously fallen to a one-and-a-half-year low in April, following the announcement of U.S. President Donald Trump’s “Liberation Day” tariffs.