While fans and existing shareholders are being asked by the board, including Mr Wallace, to put their hands in their pockets for a new open share offer, the chief executive will not be taking part.
According to new papers supporting Rangers International Football Club plc's bid to sell off 19.9 million shares, he will not participate because he has not taken any shares in the club since his appointment in November last year.
Fans questioned why the former Manchester City director has decided not to have even a small stake in the club since he arrived.
Part-time financial director Philip Nash, who was only elevated onto the board at the end of July, already has 179,000 ordinary shares and is expected to take over 54,000 more from the new offer. Chairman David Somers is to take over 14,000 more shares to take his holding up to 61,186, while director James Easdale is boosting his Ibrox portfolio by nearly a third, to 464,946.
While Rangers said that having a CEO with shares is "the exception rather than the rule in football", chief executives of Celtic and Aberdeen both have stakes in their clubs as did previous Rangers CEO Charles Green.
Mr Wallace has come under pressure after the RIFC plc board admitted its financial future will be uncertain if the new share offering ends in failure.
Rangers Supporters Association general secretary Drew Roberton said of Mr Wallace's share position: "It's not a great advert for the share issue if the chief executive doesn't have any. People will read into that whatever they will."
Fans group Rangers First has already said it will support the cash-strapped club's fund-raising bid.
The community interest company, who want to see greater fan ownership at Ibrox, said it intended to take up 150,000 shares initially, which could cost around £30,000, and are expected to look at getting more. The group, set up with the help of Supporters Direct Scotland, has more than 1000 members contributing to a share fund.