The England midfielder has made no secret of his desire for the regular Champions League football on offer at Anfield, but the Villa hierarchy rejected a reported £15million bid from the Reds earlier this month.
Barry told the News of the World: "My mind's made up, I want to join Liverpool. Villa kept saying they wanted me to stay but I have not heard from the manager for weeks."
He added: "There's no going back, it's time for me to move on. I'm desperate to play Champions League football and that's why I have to leave Villa."
O'Neill has been openly critical of Liverpool boss Rafael Benitez over his pursuit of the Villa skipper.
But despite O'Neill's public posturing, a scornful Barry insists nothing has been done to get him to remain at Villa Park.
He added: "It's seven weeks now since the season finished but while the gaffer's found time to be a pundit for the BBC at Euro 2008, he hasn't found the time to speak to me.
"Have Villa offered me anything to try to persuade me my future is at Villa Park, not Anfield? Not a thing."