The Australian international midfielder made his 'Gers debut, coming off the bench late in the 1-0 win at Dundee United on Saturday, and Arnold can see him becoming one of his country's best exports once he settles at Ibrox.
"Matty is 28 now and he is probably more ready than ever to go to Europe," the former Socceroos boss said.
"Over the last year, he has stepped into the new national manager's plans so he has gone up a level in his football.
"The two squads that I went to the World Cup with as assistant were predominantly all the same players.
"They came through in one generation but a few are in their 30s and it's time for them to move on.
"We had Harry Kewell, Scott Chipperfield, Marco Bresciano and David Carney ahead of him. Harry's moved into central midfield so that opened up the opportunity for Matt. He has taken his chance with the Socceroos. And when he plays around better players, he plays better.
"He has already made his mark in the Australia squad and has been a starting player in the last few games.
"You can see him growing every day and he will come to a big club like Rangers with a lot of confidence.
"Fans might wonder about a 28-year-old coming from Oz but I can guarantee they've signed a good lad with a good temperament."