The former Hearts defender has been given the honour of leading out the Ibrox side in their first two games of the season.
The 28-year-old, who is still waiting to be told by boss Mark Warburton if he will keep the armband permanently, sees the role as a major privilege and would love to be confirmed as former skipper Lee McCulloch’s full-time successor.
And if he does, he plans to pick the brains of Weir for his top tips on leadership.
Wallace said: “Nothing is confirmed yet but it has obviously been an honour to captain the side for the short period since the pre-season games. Until anything is concrete then I can’t really comment too much but it’s not very often that you can say you have captained the club, even if it is in the lower divisions.
“I look back on the captains that I’ve played with. Davie Weir epitomises what a Rangers player is and if the captaincy thing does come about I’ll have nobody better to lean on for advice.
“I’ve also worked with Jig (McCulloch), who was tremendous, great for the dressing room and led by example. There was also guys like Steven Davis, who led by the way he conducted himself, and Carlos Bocanegra with a wealth of international experience.
“If I was to be appointed captain and could provide half of what they did, then great.”
Rangers have impressed in back-to-back cup wins over Hibernian and Peterhead and Wallace claims much of that is to do with the fact standards have also risen off the pitch.
Revealing a new code of conduct which the players must follow, Wallace said: “There are regulations about how you should behave as a Rangers player. It is to be signed and sealed and from here on in we will be as professional as we can be.
“It’s everything you can imagine – timekeeping, leaving training equipment outside, that type of thing. There are fines and the funds go towards a charity at the end of the season. But we want to reduce those funds by acting in the right way day in day out and being the best we can be.
“The manager is big on that – being the best you can be on the training pitch, the best you can be in and around Murray Park. If you get that right then you’re going to be the best you can be on a Saturday.”
Wallace also emphasised the importance of the Rangers supporters, especially during recent matches, and said the players are looking to entertain the fans.
“It’s all about imposing our style and our tempo, the manager is huge on that,” he said. “So that’s the mind-set we need to get into here and it’s well drilled into us.
“Come match day it’s the Rangers way and it’s our tempo, our intensity. There have only been two games, there’s a long way to go.
“There was a period in the last part of the game (against Pererhead) and we were making chance after chance and the crowd made the loudest noise I’ve heard for a long time. I don’t think they quite appreciate the effect that had, because I got goose bumps. It was tremendous. I think the knock-on effect of us doing well works with the fans and vice versa.
“I can’t speak enough about how well the fans have done over these years. I think now if we can give them a positive return and send them home happy with how we have played then I think we are on to one.”