The Australian left-hander has made only one previous appearance at the Masters, missing the cut at the first major of the year in 2008.
"I should have played there more times in my career. It's something I would really like to do again," Green said after posting an encouraging one-under 71 on a difficult day for scoring in the Abu Dhabi first round on Thursday.
"My dad wasn't there with me in 2008 so hopefully I can get him there. It's always been an ambition of his to see me play at Augusta.
"When I was growing up I watched it on TV and was inspired to play golf by all the great players," said Green after finishing four strokes adrift of clubhouse leaders Justin Rose and Jamie Donaldson.
"My dad was always a big part of my junior career. He travelled with me and played with me and it would be nice to finally take him to Augusta."
Green became the first left-hander to win on the European Tour for 22 years when he captured the 1997 Dubai Desert Classic crown in a playoff with Greg Norman and Ian Woosnam.
He continued to perform steadily throughout the 2000s, achieving a career-high 29th in the world six years ago.
Green was then plagued by a wayward driver in 2011 and 2012 and is now down in 212th place.
"Towards the end of last year I worked really hard with Callaway and it's made a big difference," he explained. "We are playing golf courses now where the rough is pretty unplayable so unless you are in play you are going to struggle.
"I struggled for two years with a poor driver in the bag. Now I've got a new one and it's remarkably better, 100 percent better than it was, and I'm feeling a lot more confident.
"I feel I can sneak my way back into the top 50 in the world again. I'm a long way off but plenty of top-10 results and maybe having a win somewhere would do it pretty quickly."
He can take great heart from his showing in the Middle East on Thursday. The 6-foot-2 (1.88-metre) Australian played beautifully all day and it was just one moment of "Green greed" that cost him a much higher spot on the leaderboard.
Green found rough off the tee at the par-four 14th and, ignoring pleas from his caddie, tried to extricate himself from the long grass with a four-iron and simply succeeded in moving the ball forward 100 yards.
"My caddie wanted me to go with a five-iron and I probably got a bit greedy and tried to get it too close to the green," said the 41-year-old left-hander.
"I had one bad hole today and it cost me a double-bogey. Apart from that I can't fault my performance - it was a good base to build on, to build confidence from.
"My score wasn't really a reflection of how I played. I could easily have been three or four under."
Green, who also won the 2007 Austrian Open and 2010 Portuguese Masters, said he always looked forward to starting the year at the European Tour's Middle East swing that also takes in next week's Qatar Masters and the Dubai Classic.
"The courses here are fantastic, they are always in great condition and the weather's great too," he said. "I love it here.
"Practice facilities are always fantastic as well so it's an exciting time of the year. In recent years I haven't turned up here with much of a game but this year I feel like the basis of my game is exactly where I want it to be."