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."
Nottingham Forest's proposed takeover by a United States-based consortium led by John Jay Moores has collapsed, according to owner Fawaz Al Hasawi.