The Wrexham university lost its trusted sponsor status for overseas students in June after a Home Office investigation.
It found nearly 50,000 UK immigrants may have obtained English certificates, despite not being able to speak it.
Bosses appealed against the ban but say the UK Visas and Immigration has since asked for clarification on some issues.
Aled Roberts, North Wales AM and Liberal Democrats education spokesman, said: "We are now three to four weeks from the beginning of term and I think some certainty is needed... because some of these courses will be heavily dependent on foreign students."
The probe followed a BBC Panorama investigation into the issuing of English language certificates - on which the granting of UK student visas depends.
Glyndwr University was downgraded from its status as a "highly trusted sponsor" of student visas by the UK government, preventing it from recruiting overseas (non-EU) students.
Approximately 3,040 of Glyndwr's 8,800 students were from overseas.
The Home Office investigation found there were 230 Glyndwr-sponsored students with invalid language test results, which rose to 350 when questionable results were included.
In addition, 57 private further education colleges in the UK had their licences for admitting foreign students suspended.
In a statement, Glyndwr University said: "The UKVI has responded to Glyndwr University today on the current suspension of the university's HTS licence.
"UKVI are seeking clarification on a small number of issues. The university remains in positive discussion with the UKVI and the situation is unchanged."
Glyndwr University is still waiting to learn whether a ban on recruiting overseas students will be lifted following allegations of visa fraud.