The EU wants to agree on a deal with the UK that would make it easier for people aged between 18 and 30 to study and work abroad after Brexit.
The European Commission said it would be a limited arrangement, not a restoration of the free movement of people.
The UK already runs schemes with some non-EU countries to allow people to come to the UK for up to two years.
It says it is open to extending that to individual EU member countries, rather than throughout the EU.
A party spokesperson said it had already pledged “no return to the single market, customs union or free movement” if it takes office.
It added it wanted to improve the UK’s relationship with the EU by agreeing new arrangements for recognising work qualifications, trading food and agricultural products, and touring performers.
The EU’s free movement rules were a key part of the 2016 Brexit referendum, with the Leave campaign pledging to exit them to give the UK greater control over immigration.
The proposed EU scheme would not exactly replicate the regime, as the freedoms would be time-limited and UK participants would only be able to stay in the EU country that accepted them.
But it would significantly reduce immigration controls on young people moving between the UK and EU, with the commission suggesting no quotas on overall numbers.
The UK already has a youth mobility scheme visa allowing young people from 10 countries including Australia, New Zealand, and Canada to study or work in the UK for up to two years. However, it is not open to EU applicants.
The European Commission is proposing an EU-UK deal that would go further, lasting up to four years with no restrictions on time spent working, studying, training or volunteering.
It also says EU applicants should not have to pay the annual UK charge towards the NHS, which ranges from £776 for students and under-18s to £1,035 for workers.
The deal proposed by the commission is likely to have an impact on official immigration figures, with immigrants living in the UK for longer than a year showing up in the official statistics.
The UK turned down an offer to continue participating in the EU’s Erasmus student exchange scheme after Brexit, and has put in place a replacement, called the Turing Scheme.
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