The talks with Scotland Yard's Fixated Threat Assessment Centre (FTAC) are part of the preparations for the huge security operation surrounding the Commonwealth Games, which has been described as "the biggest in modern Scottish history".
NHS Scotland is also involved in the planning to protect VIPs and athletes, to provide psychiatric facilities for obsessed fans who break the law.
FTAC was set up in 2006 by the Metropolitan Police, the Home Office and the Department of Health to identify obsessive individuals who might pose a danger to public figures.
Deputy Chief Constable Steve Allen, security director for the Games, said it was routine for Police Scotland to work with the centre. He added: "We have clearly worked closely with them in the context of the Games in building the intelligence picture and they feed very directly into our Commonwealth Games intelligence arrangements."
He said the type of people they were interested in protecting included members of the Royal Family, high-profile politicians, athletes and "anyone in the public eye".
In terms of protecting the city physically, thousands of police officers, military personnel, stewards and private security guards will be on the streets of Glasgow as part of the security operation for the Commonwealth Games, which has been dubbed Project Servator.
It is based on an approach originally pioneered by City of London police to protect the UK capital's financial district.
Allen said: "One part of the operation revolves around the use of high-profile posters that will point people's attention to … suspicious behaviour, and will be asking people to be vigilant.
"Some of it will give messages direct to people who may have an intention to disrupt the Games, so it will make it clear to them that CCTV cameras are about and operational and that we have got staff on the ground who are out looking for suspicious behaviour.
"The City of London came up with Servator, which is a much more sophisticated approach rather than just having officers standing at traffic points in and out of the city.
"It is much more about engaging with the public and direct messaging to people that would seek to disrupt."
Allen said police would be using a "stop and engage", rather than "stop and search" approach, for example, under which officers will be making efforts to talk to the public and provide reassurance about what is going on.
He added: "It is making police officers available for the public to engage with, but also encouraging those officers to be proactive and speak to people if they look like they are lost or look like they could do with a friendly word or some help."
But he dismissed the idea this was just going back to a "bobby on the beat" style of policing, saying: "I don't think we ever lost that."
He added: "The other part of Servator is the activity the public won't see, which is a whole range of activity from plain clothes police officers who will be moving around crowds and around our high-profile transport hubs and observing again for behaviour that is out of the ordinary."
During the London Olympics in 2012, special dispersal zones were introduced to give police the power to move on "anti-social" groups of two or more people.
However, Allen said no similar measures had been introduced for the Games and that protests would be permitted.
He said: "We are really clear that part of our role and part of our function is to enable people to express their human rights, and their right to assemble, and protest and freedom of speech are things we hold very dear.
"We will be making sure our plans accommodate people's wishes in that regard hopefully without causing disruption to the Games themselves.
"We are in the process, with colleagues from government and the city council, of agreeing some pre-determined sites where we will try and facilitate protests if we can, so they are in places where we are able to keep people safe and manage the protest without too much incursion into the Games."
A spokeswoman for NHS Greater Glasgow and Clyde (NHSGGC) said health services had been a key part of the planning for the Games.
She said: "We have been working with Police Scotland and the FTAC in London to ensure that procedures are in place for NHSGGC to provide any psychiatric or other health support regarding the management of 'fixated people' during Glasgow 2014."
A spokesman for the Metropolitan Police confirmed the FTAC liaises with Police Scotland on regular basis.