The Scottish side are in Champions League qualifying action on Tuesday as they take on Belgian side Union Saint-Gilloise in the opening leg.
Centre-back Goldson, who recently penned a new deal at Ibrox, is desperate to compete in Europe's premier club competition.
Last season, Rangers missed out on Champions League football after losing to Swedish champions Malmo in the qualifying round.
"Champions League is a box I'd love to tick," said the 29-year-old. "It's the pinnacle of football and where every player wants to play.
"But at the same time I don't think that was a factor in my decision to sign my contract. Champions League has been part of the agenda for the last few years.
"Obviously last year we weren't able to make it but hopefully this year we can and over the next few years me and this football club can play Champions League football."
Goldson also came out in defence of teammate John Souttar who struggled in his Rangers debut against Livingston.
The ex-Hearts and Dundee United centre-back made an error which led to an early goal for the hosts. He was later substituted as Rangers came back for the win.
Goldson was disappointed by the online backlash against Souttar, saying: "I've been really, really impressed by him from the first week that he trained after we came back from Portugal," said Goldson.
"I was disappointed on Saturday because I saw a few things on the internet and things like that, people obviously talking bad just because he's had one game where he probably made a few mistakes.
"We've all been there, I've been there myself. I've been written off plenty times by Rangers fans but I see him every single day and see the qualities he has so I have no doubts at all he's going to be an unbelievable signing for this football club.
"He's an international player who's 25 and has played however many games in Scottish football already. We know what we signed. He's joined Rangers which we all know comes with pressure but you can't judge people off one game.
"Livingston away is obviously not the easiest place to go with the (plastic) pitch and the way they play but we've all seen his quality and I've actually been more impressed just seeing him in training than what I thought of him from playing against Hearts.
"I knew he was a good player but everything he does is so crisp with the ball and he throws himself in front of things. He's a great defender."