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First Minister Carwyn Jones said "it would be difficult to conceive" a scenario where fees are abolished in England but not Wales.
Labour's leaked draft manifesto included a pledge to abolish fees.
Grants that cover the bulk of fees are set to be scrapped from next September, replaced with support for living costs following an earlier review.
Thursday's leaked UK Labour manifesto contained a pledge that Labour "will reintroduce maintenance grants for university students, and we will abolish university tuition fees".
It is estimated that the policy would cost more than £7bn a year.
Welsh Labour leader Mr Jones said: "Clearly if there are no tuition fees in England that's bound to have an effect on the way we see things in Wales."
Universities can charge a maximum of £9,000 for a full-time undergraduate course but Welsh students only currently pay the first £3,900.
The rest has been paid for by the taxpayer - at a cost of £237m in 2015-16.
But last year the Welsh Government outlined a new system which would give all students £1,000 a year towards the costs of living, before means tested grant is then awarded
A student from a family on average income should receive £7,000 a year.
Ministers in the Welsh Government have maintained that living costs rather than fees - which can be paid back over time after students start work - are a bigger barrier to poorer students going to university.
Since 2012, a significant portion of Welsh students' fees have been paid for by the Welsh government, wherever they study in the UK.
The current Welsh education minister is the assembly's only Welsh Liberal Democrat - Kirsty Williams.
A Welsh Lib Dem spokesman said Jeremy Corbyn "isn't going to win the election".
"Living costs, not fees, are the biggest barrier to young people accessing universities," he said.
"Kirsty Williams is putting Welsh Liberal Democrats principles into action by ensuring that students in Wales will receive the equivalent of the National Living Wage while they study."
Plaid Cymru's Liz Saville Roberts said her party "has a longstanding policy to work towards scrapping tuition fees altogether so that higher education is accessible to as many young people as possible".
But she said: "The most difficult thing to conceive at the moment is a Labour majority in Westminster."