The Ireland manager is freshening up the ranks for the game against Paul Le Guen's Oman with Brady and David Meyler in line for debuts
Brady has been named in Trapattoni's starting XI for the encounter and he will make his debut along with David Meyler of Sunderland.
Trapattoni describes Brady as 'one of the best' young Irish players and thinks that the winger has the 'personality' to play in the senior ranks after moving up from under-21 level.
"Robbie Brady is one of the best junior players in our under-21 national team," Trapattoni said at the pre-match press conference. "He plays in a particular way.
"Technically, he can create. In the past we had no other like this. He's quick and very creative. He has a good personality."
"Robbie knows his quality and is a little bit cocky. I think he can do well."
Brady comes into the lineup to face Oman, unlike James McClean who has been overlooked for the starting XI following his Twitter issue arising from Friday's 2-1 win in Kazakhstan.
Trapattoni says that McClean's omission has nothing to do with his foul-mouthed Tweet after failing to feature from the bench.
Sunderland's Meyler is in line for a first Ireland cap two years on from his first call up. Two cruciate knee ligament injuries curtailed his development and Trapattoni is now happy to have another centre midfield option.
"He has good technique in midfield," he said. "He plays directly. He has good geometry. He is also physically good and tall. We followed him two years ago."
The 73-year-old has also handed a starting berth to Everton's Seamus Coleman at right back and urged the Donegal-native to prove himself in tandem with Brady.
"He can show what he can do, Trapattoni said. "He played only in the second league (Championship) as a defender. He can become well in this position. He is technically good, strong and can run for two hours."
There are no new injuries to report in the camp. Sean St Ledger will not feature on Tuesday but Alex Pearce of Reading should make his debut at centre back during the course of proceedings.
"All of our players have recovered from our travel and the game on Friday," Trapattoni said.
"We play the game versus Oman and it will be test for some of our players such as Coleman, [David] Forde, [Marc] Wilson, Brady.
"That will show us how they can integrate into our system.
"I believe that we can play a better game than our performance against Kazakhstan."
You can watch Ireland's friendly with Oman on Tuesday exclusively live through Goal.com in the United Kingdom and Australia. Click here to subscribe