Kieran Loveridge struck Mr Kelly, 18, at Kings Cross in 2012 and on Friday the State Parole Authority recommended he not be released from custody.
Loveridge, who is serving 13 years and eight months for several offences including manslaughter, was considered for parole for the first time on Friday ahead of his possible June 17 release.
But the State Parole Authority formed an intention to refuse parole.
"Our paramount consideration is always the protection of the community, and the Authority has formed the view that release on parole is not appropriate," new authority chairman Judge Geoff Bellew said.
The authority had considered reports from the Serious Offenders Review Council and Community Corrections, both of which advised against release.
Loveridge's sentence includes a 12-month term for his February 2018 assault of a bikie at Silverwater jail. He was also been involved in several other violent incidents inside prison including in March 2015 when he and a fellow inmate broke another prisoner's jaw.
He also had an affair with a female prison guard in a NSW mid-north coast prison, resulting in the guard's sacking in 2015.
Loveridge can challenge the parole authority's decision. If such a review application was successful, a public review hearing would be held in May or June.
His non-parole period expires on June 17. His maximum sentence expires on May 17, 2026.
Mr Kelly died two days after the Kings Cross attack.
In response to campaigning by Mr Kelly's parents and the media, the NSW government introduced a raft of new legislation, including mandatory sentences for some offences involving alcohol.