Dave King had a meeting at Ibrox on Tuesday and is optimistic his offer of a funding package will be accepted by Rangers.
King, in conjunction with shareholder George Letham and Paul Murray, has been in talks with the board about investing in return for a share in the club.
However, doubts remain over whether the Scottish Championship club have enough money to see out the season.
King did not wish to comment when contacted by BBC Scotland but told Sky he was hopeful a deal could be finalised.
On his way out of Ibrox the South Africa-based was asked if he was optimistic and replied: "Yes we are."
King was a director and an investor at Ibrox during Sir David Murray's ownership of Rangers and harbours a desire to put money into the club.
In recent weeks, Newcastle United owner Mike Ashley has increased his stake in Rangers to around 9% and has called for an extraordinary meeting of shareholders to remove chief executive Graham Wallace and director Philip Nash.
And Paul Murray, who like King previously served on the Rangers board, said last week that the pair were part of group holding discussions with Ibrox directors to provide funding.
Rangers are currently second in the Championship, nine points adrift of Hearts but with a game in hand.