Kyle Fox, head of KRF Capital, said negotiations had been ongoing with the Ibrox club for nine months.
It is understood her desire to buy in to the club was met with resistance from a number of key shareholders.
These include Rangers chairman Douglas Park, who has never given any indication he would be willing to sell his stake. 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."Rangers dropped a legal challenge against the Miami-based businesswoman last year after she reportedly held talks with the club's vice chairman John Bennett.
It is understood former Rangers chairman Dave King remains open to selling his 14% shareholding - after a deal to allow a fans group to purchase his shares fell through.Ms Fox said she was withdrawing her offer completely but remained open to talks in the future.
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