The Championship club had been in talks with the former owner of San Diego Padres.
However, Al Hasawi, who took control at the City Ground in 2012, says negotiations have "come to an end".
"A deal as it stands is not in the interests of the long-term future of our club," said the Kuwaiti.
"We feel strongly that we have acted in good faith on behalf of the club and its fans."
In October, it was reported that Moores, who had previously been interested in buying Premier League side Everton, was on the verge of securing a £50m deal to take an 80% stake in the East Midlands club.
The American was reportedly ready to finalise the deal on 22 December, but was waiting for final sign-off from Al Hasawi.
Two-time European Cup winners Forest are 20th in the Championship after 25 games, two points above the relegation places.
Forest had been under a transfer embargo since January 1 due to a delay in submitting audited accounts, but that was lifted on Friday.
Former Nottingham Forest and England midfielder Jermaine Jenas on BBC Radio 5 live
"The fanbase will be devastated. I am a Forest fan and am disappointed by it too. I know they were looking forward to that takeover.
"There were a few names linked with the club in terms of who would be brought in to help bring stability, growth and get the club back to where it belongs.
"This just digs deeper into the fans' hearts in terms of bad news for the season."

Its announcement came at the same time as a team of investigators for the World Anti-Doping Agency recommended Russia be banned from athletics.
Last week, French prosecutors accused the sport's governing body's ex-president of being involved.
He is alleged to have taken bribes to cover up doping cases.
Interpol's announcement follows Monday's publication of a report by an independent commission established by Wada investigating a number of individuals, including former officials of the International Association of Athletics Federations (IAAF), the agency said in a statement.
"The world police body is now working with member countries potentially linked to the inquiry, including Singapore, to seek assistance in co-ordinating a global investigative network and support the criminal investigation on the basis of the intelligence gathered by the [Wada] independent commission."
According to French investigative news agency Mediapart, the people who conducted doping inquiries for Wada believe a company registered in Singapore was used to channel certain funds that were part of the corruption operation.
As part of the inquiry, French police last week raided premises belonging to individuals and companies, Interpol said.
The Wada report was commissioned to "determine the accuracy" of allegations made in a German TV documentary about Russian athletics last December.
"The IC [independent commission] has withheld most of the contents of the chapter on the IAAF in order to not compromise the continuing efforts in respect of information provided to Interpol," the Wada report says.
"The IC is in possession of information which has been passed on to Interpol for the purposes of an integrated investigative activity, Operation Augeas. Therefore, most of the IC's recommendations in respect of the IAAF are being withheld until such time as the full chapter is released."
French prosecutors are already investigating former IAAF President Lamine Diack, who was put under criminal investigation last week on suspicion of corruption and money laundering.
He is alleged to have received more than â‚¬1m (Â£700,000; $1.1m) in bribes in 2011 to cover up positive doping tests by Russian athletes, Reuters quoted the office of France's financial prosecutor as saying.
The 82-year-old Senegalese stepped down in August after 16 years as IAAF president when Briton Sebastian Coe was elected as his replacement.
December 2014: German documentary alleges Russian doping scandal
February 2015: Diack says athletics faces 'crisis'
August 2015: Coe says IAAF will react robustly
August 2015: Wada 'alarmed' by fresh allegations
Nottingham Forest's proposed takeover by a United States-based consortium led by John Jay Moores has collapsed, according to owner Fawaz Al Hasawi.
[NEXT_CONCEPT]
International police body Interpol has said it will coordinate a French-led global investigation into doping allegations in athletics.