The Italian national, 50, died at Belmarsh high-security jail in southeast London on 5 February.
He was serving a life sentence for killing and dismembering police officer Gordon Semple, who he had met up with for sex.
Brizzi, who was HIV positive, had been put on a programme for prisoners considered at risk, a pre-inquest review hearing at Southwark Crown Court was told.
But the crystal meth addict was taken off on 28 December and on 4 January “suicide watch ceased”, senior coroner Dr Andrew Harris said.
A letter “indicating he was thinking about death” had been found in his cell, the hearing was told.
Dr Harris gave the cause of death as hanging, adding there were no injuries “implying altercation with another party”.
A noose was said to have been discovered in the cell on 6 December – when Brizzi was still on suicide watch.
It was unclear if the letter was found on 10 December or was dated on 10 December and found later, the court heard.
Dr Harris questioned the potential “non-disclosure” of the letter to staff and said it had been suggested Brizzi made the noose out of boredom.
A full inquest will open on 23 April next year and will include a jury.
The coroner said: “Given the nature of his crime we need to understand… whether he was assessed as a violent prisoner.
“It may relate to the fact he was in a single cell and whether he had been exposed to risk by other prisoners.”
Brizzi strangled police officer Gordon Semple, 59, while high during a sex session, dismembered his body and tried to cook and eat parts of it.
The former IT developer met his victim on Grindr and arranged to meet him at his flat near the Tate Modern gallery in London on 1 April last year.
A fan of Breaking Bad, he admitted being inspired by the TV series as he tried to get away with killing the officer by dissolving his flesh in an acid bath.
He was arrested after neighbours complained of a foul stench coming from his flat.
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