Wallace will hold talks with representatives of the three main fans' organisations, the Assembly, the Association and the Trust.
And officials at all three bodies hope this afternoon's talks will be the start of a long-term working relationship.
But the former Manchester City chief operating officer is set to face tough questioning about the money situation at the SPFL League One leaders.
Sky Bet Championship club Nottingham Forest have had two bids - the second believed to be for £1million - for Wallace turned down.
But there is mounting speculation the Scotland left-back will be allowed to leave if an offer of £1.5million is received.
The 26-year-old stayed loyal to the Light Blues when they dropped down to the bottom tier last season and it is uncertain if he would agree to go.
But the first-team squad was asked to consider taking a 15% pay cut earlier this month to reduce significant monthly losses at the Ibrox club.
And the former Hearts player could be put under pressure to leave in order to generate income and drive down the players' wage bill.
Rangers Supporters Association spokesman Drew Roberton stressed that fans remain concerned about the future despite being told that administration is not a possibility.
He said: "I definitely see these meetings as a positive step. I think it is important for the club to have a constructive relationship with the fans considering what has gone on in the last couple of years.
"Whoever is in charge of the club has to establish some sort of working relationship with the supporters. Let's hope that these meetings are the start of some kind of regular dialogue between us in the future.
"The club needs all the fans fully behind them if we are to get back to where we were before at the forefront of the Scottish game and hopefully this is Graham Wallace's way of ensuring that happens."
Roberton added: "But in light of the recent requests for the players to take a pay cut, and given that our former financial director said that we would be down to just £1m by April, there is real concern among the fans that the club has the money to continue to the end of the season.
"To be fair to Graham Wallace, he has stated on more than once occasion that he doesn't see a problem arising and he has access to information and facts and figures that we as ordinary fans do no have.
"But if the club do sell Lee Wallace it wouldn't go down well at all with fans. It would certainly add fuel to the fire about fans' concerns over club finances.
"If there is no risk of administration then why bother selling your best player? Selling Lee Wallace is not a move with the future of the footballing side of the club in mind.
"I am sure Lee would be one of the highest earners at the club. But would selling him really be worth it in the long run?
"It may be the chief executive's and board's thinking for the future in terms of finances. But it would be a concern from a playing point of view as we prepare to move up to the Championship next season."