Former skipper Lee McCulloch was one of 11 first-team players released at the end of last season and new boss Mark Warburton has yet to name his replacement.
Wilson would seem to be an obvious candidate for the role after he skippered Hearts to the Championship title last season, but the 23-year-old said he would always give his all for the team whether he is given the armband or not.
“It would be a great honour,” said Wilson when asked if he would like to skipper the Gers. “But I’ve been a captain before and I know that as a captain you need players around you that will help out.
“So whoever the captain is decided to be, I will make sure that I am there to support them every step of the way.”
Assistant boss David Weir confirmed the matter had been discussed but insisted the management team would not rush a decision.
“We’ve had discussions but again there has been nothing confirmed there,” said Weir, who skippered Rangers to three successive league titles before hanging up his boots.
“We are constantly talking to the players and when things are decided on that we will let you know.
“It’s an important appointment, especially at a club like this and it has got to be taken seriously. We will give it the due care and consideration it deserves.”
Wilson has come in for criticism since quitting the newly-promoted Jambos for another season in the second tier but he backed the job being done by Warburton.
He said: “I think there is something special happening here – I wouldn’t have joined otherwise.
“I wanted to be part of something successful going forward. It’s going to take a bit of time but we are putting the building blocks in place.
“The manager wants to bring in the right type of player and I’m sure they will. We just need to put our work in in the meantime.”