It follows pressure from senior officers for the monitors, which have been in the news after being used on Hollywood actress Lindsay Lohan in her numerous battles with drink, to be introduced.
The force said courts should be allowed to impose the bracelets on those serving a community sentence after committing a drink-related offence. It puts it on collision course with the Scottish Association of Social Workers (SASW), which believes any such scheme should be voluntary.
Formally responding to a Scottish Government consultation on reform of electronic monitoring, Police Scotland said: "It is reasonable to consider the use of evolving technology such as a remote alcohol monitoring service to reduce the reliance on alcohol by individuals who have committed offences and are likely to offend again as a consequence of alcohol consumption.
"However, while there may be value in extending such a scheme on a voluntary basis, without the ability to place some form of compulsory requirement for monitoring on those most susceptible to reoffending it could potentially fail to support the opportunity to bring sustainable positive change to their behaviour."
Champions in law enforcement include the police's Violence Reduction Unit.
Its director, Karyn McCluskey, last night said she believed the technology, with the right support from social workers and others, could change behaviour. She added: "Offenders can use it a tool to justify abstinence to their peers."
SASW agrees with this, but says the tags should be voluntary.
In its formal submission, SASW said "imposition could be counter-productive and create additional breach offences".
It added: "With the exception of the Alcoholics Anonymous approach, total and permanent abstention is not a model operated by any of the alcohol services in the Scottish sector, so it might not be compatible with a rehabilitation model unless it was for measuring frequency and amount rather than 'presence' alone of alcohol."
Police Scotland has also declared that using global positioning satellite systems, the kind of technology in satnavs, was a "valuable tool" as part of a wider management framework for offenders in the community.
It said: "GPS monitoring would have the capacity to build in to the management of an individual those parts of their life that are currently unsighted, for example daily movements, places frequented, anchor points."
Senior officers are particularly interested in creating exclusion zones for offenders, such as around homes of domestic abuse victims.
SASW said GPS "can only be ethically and effectively used for the 'critical few' very high risk offenders". It added: "GPS with lower risk groups would be inappropriate, largely ineffective, cost-prohibitive and ethically unjustifiable."
The UK Information Commissioner's Office said tracking should be able to be switched off when it was not needed.
Police Scotland also called for powers of arrest to be considered for every type of breach of a tagging order.
A Scottish Government spokesman said: "The consultation has closed. Responses are being analysed independently and this analysis is due to be published in the spring. We will formally respond later this year."