Police have spoken to more than 20 people in relation to NHS Tayside brain surgeon Sam Eljamel.
It follows a BBC Disclosure documentary that revealed allegations Mr Eljamel had harmed dozens of patients.
Police Scotland said it was a complex investigation that would take time.
Separately, new figures seen by the BBC show the health board paid out more than £3m on settling cases against its neurosurgery department in just five years.
A Freedom of Information request found NHS Tayside paid out £3,163,716 for just five cases against its neurosurgery department as a whole, between 2012 and 2017.
The health board said each case was investigated thoroughly and in a small number compensation was paid.
Mr Eljamel was the head of the neurosurgery department in Ninewells Hospital in Dundee - one of just four specialist centres in Scotland.
He was suspended in December 2013 and retired soon after.
The BBC Disclosure investigation found the health board did not have effective systems in place to pick up on recurrent mistakes prior to 2013.
It saw evidence dozens of people claimed to have been harmed by Mr Eljamel.
In one case he removed the wrong part of a patient's body.
Since the investigation, Police Scotland said it had spoken to more than 20 people.
A spokesman told BBC Scotland: "Police Scotland has spoken with a number of persons involved, some of whom have made complaints, and others are considering if they wish to do so.
"This is a long process which may take some time to complete. All information that has been received is currently being assessed."
Mr Eljamel, who sat on numerous government committees, was under review and investigation from June 2013 because of evidence he was making serious mistakes during surgery.
However, he was allowed to continue operating, including on patients such as Jules Rose.
She needed brain surgery but Mr Eljamel removed her tear gland instead of her tumour.
Ms Rose went to Police Scotland after the BBC investigation found NHS Tayside knew there were problems with his practice and allowed him to continue operating.
She said Mr Eljamel had been making mistakes for a long time and it was important to find out what went wrong and why NHS Tayside let him carry on.
Patrick Kelly, another former patient of Mr Eljamel, is currently suing NHS Tayside.
He said the compensation figure would increase with time as there were more cases against Mr Eljamel still in court - including his own.
He said he had been left in chronic pain and been told there was nothing that could be done.
He said: "It's absolutely shocking."
NHS Tayside said it took complaints by patients "very seriously".
It said cases often took years to settle so "reported settlements may not relate to incidents in these particular years".
It added each case was "investigated thoroughly".