Four men were last week jailed after admitting corruption charges.
Investigations into the council’s scandal-ridden property services could be reignited – following a high-profile case which saw two former council officials jailed.
Officers believe the convictions of the corrupt ex-council workers could prompt people to report further public sector wrongdoing.
And a senior detective warned that inquiries could “mushroom” if key evidence was uncovered.
Former property care officers Charles Owenson and James Costello took bribes from contractors Kevin Balmer and Brendan Cantwell in return for lucrative repair contracts for council-owned buildings.
The four men – branded “kindred corrupt spirits” by a sheriff – were jailed for a combined total of 13 years last week.
A separate investigation into the council’s property conservation section – prompted by complaints about over-inflated bills for statutory repair work on homes – found no criminal wrongdoing.
But Detective Inspector Arron Clinkscales, of the Organised Crime Unit, said officers would liaise with prosecutors if further allegations surfaced.
“We will be directed by the Crown on that,” he said. “It could mushroom, it could escalate. With public sector corruption, there are more and more people willing to come forward to speak out. I think this [the property care case] will prompt people to come forward.”
He also revealed that the probe into the property care scandal – which came after the initial investigation into the statutory notice team – was made more difficult as some of the paperwork was “unavailable”.
He said he believed the four convicted men were guilty of further fraudulent activity which could not be proved.
Conservative councillor Cameron Rose said last week’s sentencings were a “welcome milestone” – but said he feared they were the “tip of the iceberg”.
He said: “Many people are saying that there was a shredding operation within property conservation and it’s notable that the conviction didn’t directly relate to the property conservation department.
“The council has dismissed, disciplined or employed elsewhere people from that department. But I hope this is the opportunity for people who have information about what really went on to come forward.
“There will be people whose knowledge of what went on hangs heavily upon them and this is welcome opportunity for people to come forward.”
Cllr Rose added: “The implications are that what we saw at court was the tip of the iceberg. For the sake of the council and the people of Edinburgh this needs to be out in the open, otherwise suspicions will continue.”
A council spokesman said: “Police conducted a full investigation into practices across a number of council departments and found no evidence of any further criminal activity.”
The statutory repair system was suspended, then replaced in April last year, amid allegations of irregularities.
Several council staff were suspended over the controversial shared repair contracts, however no criminal charges were ever brought.