The Melbourne man, then 55, was last seen on April 12, 2012.
He was reported missing by his ex-partner, who he remained on good terms with, almost a month later.
Investigators initially believed Mr Breen had chosen to disappear on his own accord, but a recent review of the case made detectives believe he has most likely met with foul play.
This belief was cemented by the fact Mr Breen failed to attend his daughter's funeral in 2018, with family members saying it was out of character and the pair were close.
On Tuesday, police revealed his bank accounts and phone have never been accessed and there have never been any reported sightings of Mr Breen.
Mr Breen was known to police and had previously been charged with fraud offences, spending several years behind bars.
The missing man went by several other names, including Brendan Green, Brian Greer and Brendan Lacombe.
Over the past 14 years, police have spoken to a range of Mr Breen's friends and associates in an effort to try and determine his whereabouts, who may be involved in his disappearance and any possible motivation for causing him harm.
Detective Inspector Dave Dunstan said all unsolved missing persons cases in Victoria were subject to regular review, and Mr Breen's case was re-examined last year.
"There are a number of aspects about his disappearance that continue to give us cause for concern, especially the length of time he has been missing with no trace whatsoever," Det Insp Dunstan said on Tuesday.
"We know he had a number of associates who were also known to police, and while they have been spoken to over the years, this remains an active avenue of enquiry for investigators.
"While 14 years have passed, we strongly believe there are still people out there who know what has happened to Brendan, who is involved and why this has happened."
Police are also re-releasing images of Brendan in the hope that they will assist people to come forward with information about his disappearance.
