The Ibrox club reported a £23.5million operating loss for last season in their annual accounts.
The deficit for the year to June 30, 2021 was more than £7.5m bigger than the 2019-20 campaign.
Speaking at Rangers’ annual general meeting at the Clyde Auditorium on Tuesday morning, Robertson was asked if the Govan club, who won the cinch Premiership title for the first time in a decade last season, were closer to being financially sustainable.
He said: “The short answer to the question is yes, I think we are on the cusp of it.
“It has been a long road to get there because we know the investment required at the club.
“Due to the support we have had from the board and the investors who aren’t here today and the investors sitting in the audience today we are now very, very close to being in that position.
“We said in the financial report that we are looking to record a positive profit and that is looking very probable rather than possible and that is without a player sale.
“I know there is a bit of chat in the press that we need to sell a player – we don’t need to sell a player.
“What we need to do is get ourselves to a normalised position with a player trading model which is selling the right player, at the right time, at the right value for Rangers and that is something that again, we are very close to doing.
“We are getting closer to financial sustainability, we can’t keep expecting investors to shore up the club.
“I am also delighted to say that the statement within the accounts about us needing another £7.5million to get through the season, that is fulfilled already plus a bit so we are well-covered in terms of the finances of the club.
“So everyone can be confident about the financial future of the club.”
Sporting director Ross Wilson insisted Rangers will not break the wage structure to keep anyone at the club.
Speculation surrounds the future of defender Connor Goldson, who is out of contract at the end of the season and who is able to talk to other clubs in January.
However, Wilson claims he is relaxed about the issues of player contracts.
He said: “I get that player contracts is a hot topic. I get it is something that people are excited about.
“We are generally really, really relaxed with our player contracts.
“In terms of player contracts who will expire this season, there is probably three groups that I would look at.
“One, the group of our older players and we would always review those towards the end of the existing season and this season will be no different.
“I think that is sensible for both us and the players.
“The easier category is anybody who we would say is just not contributing at all, where the contract is finishing then it is safe to say those players will depart and thirdly, a player or a group of players whose contracts are up who are playing regularly.
“We have a clear contract model here, we have a clear wage structure and anybody that signs a contract at Rangers I can assure you will sign a contract within that structure and we wouldn’t be prepared to break that structure at all because that is important to us that we have a prudent way of working.
“However, it is also fair to say players can take their own view, take their own time and if they want to take a contract which is in excess of that model then that is also OK for them to take that view as well. But we are relaxed about it.”