Dunne held talks with O'Neill on Friday morning at Villa's Bodymoor Heath training complex after the two clubs agreed a fee for the Republic of Ireland international.
O'Neill wants to further boost his defensive options after completing the signing of Blackburn left-back Stephen Warnock for around £7m on Thursday.
He said: "He (Dunne) has been here today for talks. As we speak, the deal has not been completed . Normally these days there are quite a lot of issues to be sorted out but overall we have had a good chat.
"I would be hopeful he will sign for us some time on Friday or tomorrow. I am hopeful but until pen is put to paper we will have to wait.''
O'Neill insists Villa's shock exit from the Europa League at the hands of Rapid Vienna last night will have no bearing on Dunne's decision. He said: "When I spoke to Richard, that didn't seem to be the case. The truth is if he stays with Manchester City they are also not involved in European football.
"The Republic of Ireland have some big games ahead with the possibility of a World Cup in the summer and that is a long-term focus for him.''
Villa will be looking to put their season back on track when they entertain Fulham in a Barclays Premier League clash on Sunday. O'Neill admits he would have given opportunities to the club's younger players had Villa qualified for the group stages of the Europa League.
He said: "Regarding Europe, my own view, in the cold light of day, is that it is not the end of the world what has happened. It is disappointing we are not through. My disappointment is we won't have European football again for our younger players.
"Had we gone through I was going to give some of the younger players the European experience home and away sprinkled with the experience needed to get through games. That will now have to be shelved.
"But we can put last night behind us. We performed well in the game and added to the performance at Liverpool on Monday, it will give the players a lift in confidence. The crowd were also excellent in supporting us to the bitter end and hopefully, against Fulham, we can utilise all these things.''
Warnock could make his debut against the Cottagers with O'Neill stressing the importance of the 27-year-old's versatility. He said: "Stephen has loads of ability and being versatile is very important. He can play in a number of positions which has been the case at Blackburn. He actually played against us in midfield last season and I am just delighted to have signed him.''
Central defender Curtis Davies is a doubt to face Fulham after suffering a further shoulder setback during the Vienna game and Villa will use the international break to decide whether he will need surgery.
Davies was first troubled by the problem during his time as a West Brom player four years ago and the shoulder has popped out of its socket three times in the past three weeks.
Striker Gabriel Agbonlahor could earn a return to the starting line-up after being rested against Vienna although John Carew impressed in his first appearance of the season and scored the second goal for his side.