"I am hopeful Arsene Wenger will let Liam do the job as well as his Arsenal commitment," the 68-year-old said.
"I knew Liam as a player and I asked him if it was possible for him to work with me a bit.
"He speaks good Italian and he knows the players. We can work together but not all the time because Liam has a good job at Arsenal."
Qualifying for the World Cup in 2010 will be hard but it should be possible for Ireland to come first
FAI chief executive John Delaney said O'Brien's financial offer was "a pivotal moment in the recruitment process because it enabled us to raise the bar even higher than intended".
O'Brien, who made his billions in mobile phones and media, has offered to cover half the cost of the new managerial team.
"I'm a great believer if you hire the right people you get the right results," said O'Brien.
Delaney added: "Everyone acknowledges the senior national team has not achieved to the extent that we would all like over the past five years but we're now entering a new era with a manager whose record is among the most successful in Europe.
"He's widely acknowledged as one of the most outstanding and successful coaches in the modern game."
Trapattoni has vowed to lead the Republic to the 2010 World Cup finals and is confident they can finish top of a group which also includes his countrymen.
Italy will be at home to the Republic on April Fool's Day in 2009 with the return game taking place at Croke Park six months later on 10 October.
"Ireland are not a second-rate team, they are supposed to be a first-rate team," insisted Trapattoni, who managed Italy from 2000 to 2004.
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