The proposal has been met by an instant backlash...
Robert Goodwill from the Conservative Party raised the prospect that a scheme imposing such a charge on recruitment from outside the bloc, due to come into force later this year, could be extended after the UK finalises its exit from the EU.
The suggestion was met with fury by the European Parliament's chief Brexit negotiator Guy Verhofstadt.
He wrote on Twitter: "Imagine, just for a moment, what the UK headlines would be, if the EU proposed this for UK nationals? Shocking."
Freedom of movement rules are seen as likely to be a key stumbling block in Brexit negotiations.
The British Government has said it will seek controls over the numbers of people coming into the country, but the shape of any post-Brexit immigration system has yet to be outlined.
Mr Goodwill spoke about the possible widening of the non-EU workers scheme when he appeared before the Lords EU Home Affairs sub-committee.
As it stands the scheme will apply an annual charge of £1,000 for every skilled worker a firm employs from outside Europe, from April.
For a four-year contract it would mean employers facing a £4,000 fee.
Mr Goodwill told peers: "That's something that current applies to non-EU [...] That may be something that's been suggested to us that could apply to EU.
"But we are not in a position to really speculate as to what the settlement will be post-Brexit negotiations."
Mr Goodwill also indicated that a scheme to allow entry for some seasonal agricultural workers was being considered.
Net long-term international migration from the EU and the rest of the world has been running at near record levels of more than a third of a million - significantly more than the UK Government's target of under 100,000.
A number of options for an immigration system have been suggested since the Brexit vote, including a work permits regime or a so-called "emergency brake" approach.
Mr Goodwill said a number of models are being explored, but told peers it would be "pointless" to speculate ahead of the negotiations.
Prime Minister Theresa May's spokeswoman said Mr Goodwill had said "there are a number of options that could be considered".
Liberal Democrat business spokesman Don Foster said such a move "would kill off British businesses", adding: "The Conservatives used to represent business interests, they have now sacrificed them on the altar of populism."
Business groups were also quick to dismiss the idea. The British Hospitality Association warned it would increase costs for firms and lead to higher prices for consumers.