Goldson has moved to Rangers from Brighton and Hove Albion in the summer transfer window for a fee reported by The Daily Record to be worth £3 million.
Rangers manager Steven Gerrard has not yet announce who his captain will be for the 2018-19 campaign.
Goldson told The Glasgow Evening Times: “It would be unbelievable [to be captain] but at the same time that is his decision to make.
“There are people that have been here a lot longer than me, people who have already been captain.
“So I can’t sit here and say ‘yes, I want to be captain of the football club’. It would be amazing but there are other candidates and other people who could be captain. It’s not for me to talk about at the minute.”
Goldson is a very good defender who will be a key figure in the Rangers team for the 2018-19 campaign.
It would make sense for Liverpool legend Gerrard to hand the 25-year-old centre-back the captain’s armband, but the former England international midfielder should look at other candidates as well.
It is quite encouraging that the former Shrewsbury Town star is open to become the new captain of Rangers, and it underlines his confidence in himself and his desire to take responsibility.
Rangers will be aiming to compete with Old Firm rivals Celtic for the Scottish Premiership title next season.