Newly-appointed boss Ronnie Moore said after Saturday's 1-1 draw with Oxford that it was a "possibility" the striker could join Pools.
But in a statement released on Sunday afternoon, the club said they "do not intend signing Ched Evans and, for the avoidance of doubt, will not be doing so, irrespective of his obvious ability as a football player".
Moore, who was given the job on Tuesday, was asked whether he would be willing to bring the 25-year-old to Victoria Park and the club have moved to clarify those comments.
The statement added: "This story has emerged following an unsubstantiated internet rumour which the manager was asked to comment upon.
"The manager responded hypothetically to the situation by stating 'if it could happen I would want it to happen'.
"This response was based upon the player's obvious ability as a footballer and as such as then been headlined by the media without asking the club for their official position.
"The club can fully understand the concerns of supporters and the general public and regrets any misconception portrayed.
"After a highly positive week at Hartlepool United following the takeover by new owners and the appointment of a new manager, the owners are saddened by this unfortunate turn of events and wish to draw a line under it immediately."