Evans, 25, was released in October after serving half of a five-year sentence for the rape of a 19-year-old woman in a hotel room in 2011.
Moore, who took charge of the Football League's bottom club this week, has confirmed his interest in Wales and ex-Sheffield United striker Evans.
"It's a possibility. If it could happen, I'd want it to," he said after Saturday's 1-1 home draw with Oxford.
"He is a proven scorer; he's served his time and the boy wants to play football."
Sheffield United retracted an offer to allow Evans to train with them last month following strong local opposition, but 61-year-old Moore insists he is willing to offer the forward a route back into football.
"If there is a chance he might come here, I don't see any reason why he shouldn't," he continued.
Moore who is an experinced manager is not adverse to contraversy himseld and was dismissed by Tranmere Rovers in April after he admitted breaking FA betting rules
However, Moore added: "He has made a mistake and maybe he hasn't apologised in the right way - and I know he has an appeal case pending - but if he gets on the park, he would go a long way to getting us out of trouble."
His appointment by Hartlepool came on the same day as TMH 2014 Limited completed their takeover of the north-east club from previous owner Ken Hodcroft.
But the move for Evans is bound to strike a furore and Hartlepool's Labour MP Iain Wright was quick to brand Evans a "pariah" saying 'Signing him would send the wrong message to young fans..'