Leaving Cert students face having their results withheld if there's evidence of interference in the calculated grades process by parents or the students themselves.
The sanction is being looked at as part of new legislation the Government is currently working on.
A spokesperson says "more serious consequences" are also being considered, and the details will be published shortly.
Labour Party education spokesperson Aodhán Ó Ríordáin said penalties for lobbying teachers are necessary.
He observed: "Clearly last year's experience would tell us there was a level of canvassing going on, and a level of pressure put on students.
"This was something that teachers were uncomfortable with.
"Given the fact there's a greater timescale now for that pressure to be exerted on teachers, it's only fair there's legislative underpinning of this process and the sanctions are known well in advance."
While his party will back the legislation, Deputy Ó Ríordáin said they'd also have liked to see an independent review of last year's Leaving Cert process so more lessons could be learned.
Meanwhile, students will be able to register their preferred option for this year's Leaving Cert from later today.
The self-service portal opens at midday, with students able to indicate whether they wish to sit the exam, take calculated grades, or both.
Registration closes next Tuesday, but will open again around the end of April when they'll be asked to confirm their choices.