Gillett arrived earlier this week in Riyadh sparking speculation that the visit will push towards the conclusion a deal with F6 owners, who include Saudi Prince Faisal bin Fahd bin Abdullah and Saudi businessman Majed al-Hugail.
"The purchase of a stake in Liverpool has not been discussed throughout Gillett's visit, not for even five minutes," F6 Deputy Managing Director Gassim Hamidaddin told Reuters.
"The discussions are now on hold. The idea of buying a stake in Liverpool was put on the table in September but since then nothing happened," he added.
Investors from Gulf Arab countries have shown growing interest in acquiring football clubs in the English Premier League.
In August, United Arab Emirates' investor Sulaiman al-Fahim completed a takeover of Portsmouth Football Club before reselling later a large stake in the club to a Saudi businessman.
Abu Dhabi United Group for Development and Investment bought Manchester City last year.
F6 is focusing on implementing the terms of a contract it signed last month with the George Gillett Group that would lead to opening Liverpool academies in the Middle East and North Africa and develop race tracks to introduce NASCAR motor racing to the Middle East.
"That's what was discussed during Gillett's visit," Hamidaddin said.
Liverpool are keen to raise fresh cash to help challenge for top footballing honours and fund the construction of the new stadium, as well as finance debt estimated at 245 million pounds.
Liverpool is England's most historically successful club, with 18 league titles and five European Cup triumphs.
Last month, Al-Riyadh newspaper quoted F6 Chairman Prince Faisal as saying he was willing to pay between 200 million and 350 million pounds for between 25 and 50 percent of the Anfield Stadium side.
Gillett and fellow American Tom Hicks - Liverpool's co-owner - have had a stormy relationship since purchasing the club for 218.9 million pounds in 2007 and neither wants to sell his stake to the other.
The two men were in talks in January to sell the club for 500 million pounds including debt to investors from the region, including Kuwait, but talks broke down over price, one of those involved said.
