The University of Exeter said in a statement: "We have informed affected colleagues and are updating students and our wider community.
"We hope to achieve these changes through voluntary measures and will continue working closely with our community and trade unions to avoid compulsory redundancies wherever possible."
It added that while Exeter "remains in a strong position", rising costs, decline in tuition fee income, underfunded research, and a sustained drop in international student demand mean action must be taken.
"These changes are intended to secure the university's long-term sustainability, protect our teaching and research excellence, and ensure our activities remain aligned with future priorities," the statement said.
It said the current proposals included a reduction equivalent to about 150 full-time roles.
The EUCU fear the potential changes place "well over 500 staff - 14% of all academic staff - at risk of compulsory redundancy in the run-up to Christmas".
A spokesperson for the union said: "These proposals represent both a stunning failure of leadership on the part of the university's senior management and governance, and a reckless attack on an institution that is critical to the Westcountry's regional economy."
They added that although staff across the academic body were impacted, the cuts were "disproportionately concentrated in the Faculty of Humanities and Social Sciences (HASS), where 85% of all staff placed at risk of redundancy (445 out of 523 FTE) are based".
The spokesperson said: "If they go ahead, student experience will suffer enormously, and both teaching programmes and research culture will be damaged beyond repair.
"The rationale for this disproportionate targeting of the very disciplines to which Exeter largely owes its membership of the Russell Group has not been clearly explained to us."
Follow BBC Devon on X, external, Facebook, external and Instagram, external. Send your story ideas to spotlight@bbc.co.uk, external.