The proposal, which has emerged from the authority's discipline working group, will apply to the parents of children as they register to start school.
However, with the proposed consultation likely to finish at the end of June, by which time next year's intake of new pupils will already have registered, only parents of children moving to a new school during the school year will be affected initially.
Steven Purcell, education convener, said: "If a parent doesn't want to sign up, there is nothing we can do about that. We can't make it a statutory part of schooling. But we are hoping that parents will sign up to it and it will be seen as a partnership.
"The commitment to the contract should not be seen as a negative thing but as positive. We are saying: 'This is what we want to do at this school and we need your support to create the right kind of ethos in the school.' " Councillor Purcell added that the discipline group had heard from teachers that they did not receive support from some parents on discipline and behaviour issues. He hoped that, by introducing behaviour contracts, parents would be more likely to take responsibility for their children.
Ronnie Smith, general secretary of the Educational Institute of Scotland, said: "I don't think behaviour contracts are a magic formula or panacea that will solve the problem but they are worth trying. If there is a message getting across that behaviour is a priority issue and it permeates the consciousness, then that's useful."
Meanwhile, the council's policy and resources committee has backed a proposal for the authority to continue until December 2006 to manage Kerelaw secure unit, for young people with behavioural problems deemed to be at risk.
Last year, Glasgow closed its residential school at Kerelaw in Ayrshire, and said it wanted to relinquish management of the secure unit after allegations about staff conduct and poor inspection reports at the open school and secure unit. The council's management of the secure unit will continue until the Executive provides alternative places in new units.