The regulatory body for teachers is considering plans to scrap the requirement because of the difficulties in securing checks from some countries.
The General Teaching Council for Scotland (GTCS) argues that securing such checks is particularly unreasonable in some cases where teachers are seeking asylum from countries where their lives are at risk.
However, the proposal has sparked a backlash from parents and teaching unions, who argue that the GTCS should be performing as many checks as possible.
More than 500 teachers from overseas have applied to work in Scottish schools over the past five years.
Eileen Prior, executive director of the Scottish Parent Teacher Council, said: "The regulation around disclosures for anyone working with children in Scotland is something we often say is overdone, but in this case we believe parents expect that anyone working in a school would be checked.
"Parents would be surprised that some teachers coming from other countries would not be asked to provide criminal-records checks.
"There may not be a level playing field, but removing checks from those who can provide them does not seem to be a reasonable solution."
Iain Ellis, chairman of the National Parent Forum of Scotland, added: "We believe that checks should be as robust as possible for all teachers working in all Scottish schools and that no-one should be exempt from these checks."
Larry Flanagan, general secretary of the Educational Institute of Scotland teaching union, also expressed concern.
"Clearly, the suggestion of some overseas applicants to the GTCS register potentially not being criminal-record checked is an issue that raises concerns.
"Taking all reasonable steps to background-check all applicants is very important."
Mr Flanagan said the setting up of a new "exceptional admissions procedure" should be explored for teachers coming to Scotland from countries that lacked a suitable background check system.
A GTCS spokesman stressed that no decision had been taken to stop the practice.
He said: "Providing a criminal record check is not straightforward because many countries do not hold criminal records.
"In addition, there are crimes in some countries which are not crimes in the UK."
The spokesman said all overseas applicants would continue to have to meet the GTCS standards, show evidence of relevant qualifications, provide a reference from their last employer and sign a declaration that they have no criminal convictions.
He added: "This is a complex issue which GTCS, as the teaching regulator, is duty-bound to review from time to time. Our professional regulatory assurance committee is looking into the practice of carrying out overseas criminal record checks and will report back its findings in due course."