The defender was given the armband at the start of the season.
The 28-year-old became the Scottish Championship side's skipper at the start of this season in the wake of Lee McCulloch's departure in the summer. And while his spell as leader is in its infancy, he mentioned his predecessor as well as two other great captains in the club's history - including the current assistant manager - as players that he is keen to emulate at Ibrox.
"I'm well aware that in Rangers' history I'm the least off in terms of being successful and winning medals," he told The Scottish Sun reports.
"I go back to Lee McCulloch, who was part of successful teams here and won loads of things, then Davie Weir and Richard Gough, who were also very successful.
"The dreams and aspirations for me are to try to become like these people. Will we be as successful as these Rangers teams from the past? I don't know, but maybe. Will I be as successful as these captains? I don't know, maybe."
Although the left-back is yet to lift a trophy as captain, he could finish the campaign with as many as three pieces of silverware.
The Scottish Championship title is almost secured as they sit 11 points clear with just seven games to go. Meanwhile, they have a Challenge Cup final against Peterhead to look forward to in April, while they have also made it to the last four of the Scottish Cup where Old Firm rivals Celtic stand between them and another final.
And if Wallace is able to lead the Gers to success on all three fronts, he will have made an excellent start in his attempts to create a legacy to rival some of the club's greatest captains.