"Hopefully I can put in a big performance on Saturday and make his mind up for him," said Cooper, 28, who will make his first start for Wales since November 2005.
"I've played in some big matches in the past but, considering where I am at the moment, this is probably the biggest game of my life.
"Getting over the nerves and the pressure is going to be a difficult thing, with so much at stake, but I've got to try and get out there and enjoy the experience.
"We've got to go out and give a good team performance, which will give us all the best opportunity to be selected for the World Cup.
"I'm sure if I went out there and tried to show off, it wouldn't be good for the side and I'd be found wanting."
Cooper will also be anxious to bury memories of his last performance in the red jersey, when his mistake arguably cost Wales victory over Australia in Sydney.
Cooper came off the bench in the first Test against the Wallabies. Wales were leading 23-22 and seconds from a famous victory when a poor clearance gifted possession back to Australia.
A second effort then sliced into touch, presenting Australia with a platform to attack from the Wales 22 and Stephen Hoiles scored the winning try with the last play of the game.
Cooper was singled out for blame but he is determined to put the disappointment behind him and prove to Jenkins he can make a valuable contribution over the coming weeks.
He told the Western Mail: "I'm just looking forward to this weekend now to put a marker down again, to get out there and just enjoy playing for Wales. You've got to try and take every chance you can with two hands."