Kyle Fox, head of KRF Capital, had been in discussion with the Ibrox club for the past nine months but has now walked away from the negotiating table after failing to reach an agreement with existing shareholders.
Ms Fox told BBC Scotland: "Our interest was predicated on certain conditions being met - those conditions were not met. Our letter of interest included gaining anti-dilution rights protection, two board seats and access to the data room and management interviews. All were denied."
The broadcaster also claims that Ms Fox encountered resistance from a number of key shareholders including Rangers chairman Douglas Park, who was reluctant to sell his stake to the Miami-based investor. She has now backed out of the takeover bid but has left the door open to resume talks in the future.
Rangers launched legal action against Ms Fox last year over a potential breach of trademark by using the club logo in her attempts to gain investors but the case was subsequently dropped by the Ibrox club.
Former Rangers chairman Dave King, who voted against the re-election of Douglas Park as chairman at the club's last AGM, is said to remain willing to sell his 14 per cent shareholding after a deal to allow fans group Club 1872 to purchase his shares fell through.
Rangers fans have protested against the current power-brokers at Ibrox in recent weeks over the perceived poor recruitment. Supporters group Union Bears refused to take up their seats for the Scottish Cup win over Raith Rovers on Sunday after having banners confiscated.
Meanwhile, Mark Hateley has warned Rangers manager Michael Beale he will face “tsunami” of pressure if he loses to Celtic in the next Old Firm clash at Ibrox next month.
“If he loses the league match on April 8, the tsunami will only get closer and closer until it comes crashing down – but that’s what being at Rangers is all about,” said the former Gers striker. “You have to handle that pressure.
“Of course, if Rangers can finish the season strongly, win the semi-final and lift the Cup it will be a huge springboard for next season. Lose, and the opposite is true as Celtic will be strolling to a treble.”