The KRF Capital owner wanted to purchase a controlling stake in the Ibrox club.
Talks had gone on for nine months, but key shareholders of the Scottish Premiership club have frustrated her efforts.
Rangers chairman Douglas Park has never indicated the willingness to sell his 12% stake.
Fox wanted to gain anti-dilution rights protection, two board seats and access to the data room and management interviews.
However, all her efforts and attempts were denied.
Rangers also dropped a legal challenge against her last year after she held talks with vice chairman John Bennett.
The club’s former chairman Dave King saw a deal to allow a fans group to purchase his 14% shares fall through.
However, he remains keen on cashing in on his stake.
While Fox has completely withdrawn her offer, she is open to reopening talks in the future.
Stuart Gibson and non-executive director George Alexander Taylor own a 10% stake each.
Rangers supporters group Club 1872 and Bennett own 5% each.
The majority of them are not keen on selling their shares.
Fox wanted to become the club’s majority owner, but that has proven difficult.
Rangers could do with major squad investment having struggled to challenge Celtic on the domestic scene.
They won the Premiership title in 2020-21 to stop the Hoops from winning a tenth consecutive title.
However, Celtic reclaimed it last season and have gone nine points clear at the top of the table after 28 games this term.
- Postecoglou confirms huge injury blow for Tottenham ahead of Crystal Palace clash
- FA Cup quarter-final TV picks confirmed, ITV will show headline fixture between Man Utd and Liverpool
- Preview: Man City vs Man United – stats, team news, line-ups
- Crystal Palace shareholder John Textor slams Premier League financial rules
- Conor Gallagher determined to stay at Chelsea despite contract stand-off and Tottenham interest
- Eric Dier makes permanent switch to Bayern Munich from Tottenham
- Premier League manager of the month nominees for February revealed
- Paul Pogba receives four-year ban for doping
- Man United fans in uproar as Old Trafford relocation plans spark outrage
- Liverpool to make one last attempt to bring back Michael Edwards to lead post-Klopp rebuild