The 71-year-old is due to find out on Wednesday whether his application to be released from jail has been granted, The Sun reported.
If it is approved by the Parole Board, Noye could be released within three months.
Legal experts say it is "highly likely" that he will be freed on licence, the paper added.
Noye is serving a life sentence for murdering 21-year-old Stephen Cameron in a road rage attack in Swanley, Kent, in 1996.
He fled to Spain after the killing, but was brought back and convicted in 2000. A judge recommended he serve a minimum of 16 years.
Speaking of the killer's potential release, Mr Cameron’s dad Ken, 72, told the Sun: “All we ever wanted was justice. Life should mean life for him.
"The only way Noye should be allowed out is in a wooden box.’’
Noye was transferred to Standford Hill open prison in 2017, prompting outrage among politicians and Mr Cameron's family.
Noye was acquitted in 1985 of murdering detective John Fordham.
He was later convicted of handling stolen goods, and served eight years in prison, before being released in 1994.
He carried out the road rage killing two years later.
Noye had claimed he stabbed Mr Cameron in self-defence.