Canadian Gillett and American business partner Tom Hicks are unpopular with some Reds fans after their disagreements with manager Rafael Benitez and their controversial re-financing of the club.
Speaking to a sports radio programme in Toronto, Gillett said: "This partnership has been unworkable for some time."
He also said he and his wife "receive many phone calls in the middle of the night threatening our lives".
Gillett initially wanted to buy the club on his own in January last year, but brought in Hicks' financial muscle when he could not do the deal himself.
And he claims Hicks not only failed to take up an offer to buy his share, but also tried to stop Gillett selling to DIC.
Gillett has also revealed that instead of selling the club, he may try to buy out Hicks and take full control.
Gillett said: "This partnership has been unworkable for some time.
"But not because of us - we have tried to be co-operative, we have tried to be supportive but when your public persona is more important than the facts that makes it difficult to have a rational relationship.
"We were very fair. We gave our partner (Hicks) a long period of time to try to make arrangements to buy us out.
"We didn't put pressure on him but he ultimately did not get to the finish line.
"In the meantime, because of the things he said, the fans' reaction has been so negative towards him - and towards us if we sold to him - that has now made that an untenable alternative for us.
"He threatened to block me selling to Dubai - that was certainly one of the things that made the fans upset.
"Lord knows DIC have the money; with oil prices going up every day, that's not an issue. They certainly have the history and they are fans.
"I think they would have been very responsible owners.
"But making that not possible or difficult didn't endear people to the fans."
Gillett revealed he has received abuse which he believes has been brought about by Hicks' comments in the media.
"We get as many as 2,000 emails a week," he said.
"Ninety five per cent of them have been directed at some of the comments made by my partner. And five per cent aimed at both of us - 'Go Home Americans!'
"The thing that angers fans the most is the prospect I might sell even one share of my stock to my partner.
"They do not want him to have any controlling interest in this club - they do not even want him to have any ownership in the club.
"As a result of that - and it's been very difficult for my wife with the amount that I travel - we receive many phone calls in the middle of the night threatening our lives, death threats."
Gillett continued: "A number came to the office and my son Foster and daughter-in-law Lauren have received them.
"It's interesting the calls are not against my wife or myself or my son or my daughter-in-law, as much as they are against us selling to our partner.
"So we are rethinking that. Frankly, I don't think it's fair for me to put my family in that kind of danger.
"So instead of thinking about selling, I might think about buying."