Former Italy boss Giovanni Trapattoni is now understood to be the FAI's preferred choice for the position.
Venables remains in contention although he is believed to be unhappy at the length of the process.
"Personally, I'd probably prefer somebody we can communicate with, being Venables," added Dunne.
"I don't know how good Trapattoni's English is and we only have two games after this one (Wednesday's game against Brazil) before the start of the World Cup campaign.
"We need somebody who can get his point across very quickly."
Dunne also suggested that he was concerned that the confusion over the identity of the next manager could lead other players into questioning their international future.
"I know there is, so it needs to be sorted out before more people go the way of Steve Finnan and Andy O'Brien."
Finnan announced his international retirement last month while O'Brien called time on his Republic career over the weekend.