Pools had appeared set to complete a double raid on the Irish outfit, with a deal also agreed for striker Denis Behan.
However, they now look set to miss out on Healy after Ipswich boss Roy Keane signalled his interest in the 29-year-old.
The former Celtic and Sunderland man is now expected to complete a move to Portman Road this week.
Hartlepool director of sport Chris Turner has admitted his disappointment at the saga, but accepts there is little he can do to prevent the player from moving elsewhere.
"We came very close to signing Colin Healy," he told the Northern Echo.
"But we have come up short. It is annoying because we have worked hard for two months on Colin Healy, only for Ipswich to play Cork on Sunday and decide they want him."