The Independent, owned by Russian businessman Alexander Lebedev, axed the weekly education supplement, published on Thursdays, earlier this month.
The move, likely to save costs at the national newspaper, means that editorial content from the supplement has been folded into the main newspaper, and the role of education supplement editor has been made redundant.
According to the National Union of Journalists (NUJ), compulsory redundancy has been proposed in the case of Hodges.
A ballot on whether to go ahead with industrial action is expected to be held next month.
Hodges, who is still working at the newspaper, has been with The Independent for 11 years.
The newspaper has published its education supplement for more than 10 years. The Guardian publishes a weekly education supplement on Tuesday. The Times Educational Supplement, owned by TSL Education, is also published every week.
It is unclear if the move to axe the supplement will impact on The Independent's commercial relationship with UCAS Media, the advertising and marketing arm of the university admissions service.
The Independent publishes the annual clearing listings and a number of other student-related magazines for the student application's body.
The commercial partnership between is thought to be up for review next year.
The move comes as Andy Mullins, managing director of The Independent and the London Evening Standard, carries out a and The Independent on Sunday.
The findings of the strategy review, expected in September this year, could lead to an overhaul of individual departments.
Executives at The Independent declined to comment, as did Hodges.
Fiona Swarbrick, national organiser in publishing department at the NUJ, said: "The chapel has indicated that it will take industrial action against compulsory redundancies, but we hope that a resolution can be reached."
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