Many parents of Primary 7 children are "worried sick" due to uncertainties about how they will transfer to post-primary schools.
That is according to the principal of a primary school in Lisburn.
A teaching union has also said that primary principals are "at a loss" over how to advise parents about the transfer process.
Transfer tests were cancelled for 2021 and most grammar schools have not yet said how they will select pupils.
All post-primary schools have to provide the Education Authority (EA) with admissions criteria by Friday, but it is still unclear whether some grammars will use academic criteria.
Parents will then begin to apply to schools for their children to transfer to in March.
That has led some primary schools to offer parents the choice of their children taking standardised tests in case some grammars use a pupil's primary school results as part of their selection process.
'Period of disruption'
In a letter to parents of his Primary 7 pupils, the principal of St Colman's Primary in Lisburn, Stephen Baine, said he knew many were "worried sick" about the uncertainty around how their children would transfer from primary to post-primary schools.
"It has been such an awful period of disruption for our P7 children who have worked so hard," he said.
"Post-primary schools across the country [those who rely on the results of the GL/AQE examinations] must decide on the admissions criteria they wish to use to admit pupils in September 2021 if they are oversubscribed.
"Primary schools are not privy to these discussions or decisions and, like parents, we find out when the respective criteria are published by the Education Authority."
He said that in St Colman's, P7 children normally took standardised tests in maths and English in February each year.
"If post-primary schools require this data for applications, it will be provided," he said.
Mr Baine said that in order to support parents, the school would try to hold those tests in mid-February if children returned to school then.
If schools do not reopen as planned, he said the school would also look at whether tests could be held safely.
"This will mean that parents will have up-to-date standardised scores to support their child's application to those schools who may require them as part of their admissions criteria," he said.
Millennium Primary in Saintfield had also previously offered to provide the option to parents for their children to sit standardised tests.
Its principal, Barry Corrigan, said that had been as a result of requests from parents.
"All primary schools are being faced with difficult decisions at this time of great uncertainty," he said in a statement to BBC News NI.
"Given the difficult year that all families are having, we are determined to give parents and children as much information as possible to support them in making their decisions."
Jacquie White, of the Ulster Teachers' Union, told MLAs on Stormont's Education Committee that primary schools had been calling "for some time" for a contingency plan for the transfer process this year.
"We all accept that this has been a contentious issue for many years, but I can assure the committee that in this context, this call was not grounded in ideology but rather in general concern for the health and safety of our children, parents and the wider community," she said.
"It's highly regrettable that ideological differences stood in the way of actually focusing on a resolution for the children."
She said schools now "have absolutely no clarity and they are at a loss as to how to advise parents how to proceed" and staff are "very concerned about the role that they may be asked to play in any academic selection process".
But Ms White said that primary schools would provide data about an individual child to their parents if requested.