City bosses currently only accept petitions from the public by hard copy letter.
But David McDonald, the nationalists' business manager on the city council, wants those who have a complaint or a suggestion to be able to go directly to city leaders without "jumping through hoops".
The SNP councillor is proposing an online form that would-be petitioners could fill in. His political opponents today said they would look at the idea.
Mr McDonald said: "The SNP led in Glasgow with calls for a petitions committee for the city. While we are happy that our proposal was accepted, we feel that there are a number of steps which could be taken to improve the committee's work.
"We believe, fundamentally, that an e-petition system - like the popular one operated by the City of Edinburgh Council - will make the petitions committee more accessible and responsive to the issues that matter to Glaswegians.
"We have also called for a review of the Public Petitions and General Purposes Policy Development Committee procedures more generally and hope that the Council will do all that it can to make our petitions committee more robust.
"Our city deserves a petitions committee that everyone can access and which can genuinely effect change in our city."
Council insiders stress that Glasgow's system - in some ways - is already more open than Edinburgh's.
A Glasgow council spokesman said: "We are currently undertaking the annual review of the processes for the petitions committee, as was scheduled when the committee was first established.
"As part of that review, we will be looking at the merits of an e-petition system. It should be noted that where Glasgow requires a petition to be endorsed by 25 signatories other local authorities with a petitions system look for 500 signatures.
"Also where other authorities only accept petitions from people registered on the electoral roll, Glasgow welcomes petitions from under 18s."