Palios said he had twice been contacted by people on behalf of Evans about possible talks but refused to pursue the idea.
Evans, 25, wants to return to football after being released from prison last month
He served two and a half years of a five-year sentence after being found guilty of raping a 19-year-old woman in 2011.
Evans continues to protest his innocence and has lodged an appeal with the Criminal Case Review Commission.
He was initially given permission by former club Sheffield United to return to train with the club at the request of players' union, the Professional Footballers Association.
But following a backlash from Blades supporters, sponsors and patrons opposed to Evans' return - 160,000 people signed a petition against it - the club retracted its offer last week.
Palios, former chief executive of the Football Association, and wife Nicola took control at Tranmere in August.
He said in a statement released to the Liverpool Echo: "Tranmere has not been approached by Ched Evans or his management team to discuss him joining the club.
"However, on two occasions persons with a connection with Ched Evans offered to facilitate a discussion if I wished to pursue that.
"I strongly believe in the general principle that people have a right to rehabilitation after serving a sentence for a crime.
"However, I also take the view that whether any particular club would wish to employ someone who has been convicted of a very serious crime is a subjective decision for the club to take after considering all the circumstances, and that there is no simple right or wrong answer.
"Nicola and I are trying to re-establish the brand of Tranmere as a family-friendly club and bringing Ched Evans in would clearly have alienated a significant number of supporters.
"It would also have inevitably embroiled the club in much controversy and distraction, at a time when we need to keep a complete focus on rebuilding the club and setting firm foundations for the future.
"I therefore took the view that it would not be in the best interests of the club to seek a dialogue with Mr Evans, notwithstanding his undoubted footballing talents.
"Neither I nor the club will be making any further comment on this matter."
Tranmere allowed Clayton McDonald, who was acquitted of rape when tried alongside Evans, to join the club on non-contract terms earlier in the season, but he was released after just one appearance.
Source : PA