From April, recruiting non-EEA skilled workers will see employers pay a charge of £1,000 per year.
Since Goodwill's comments, Home Office officials have stressed that extended the charge to EU workers is only one option under consideration.
In addition, any move to do so would require primary legislation, and would therefore require the approval of MPs in the House of Commons.
However, business groups remain furious over the proposals.
British Chambers of Commerce director general Adam Marshall said the move would make the UK less attractive to investment and be harmful to overall economic growth.
“Businesses already report recruitment difficulties, and are struggling to find all the skills they need here at home. A levy on EU hires would add unnecessary expense and bureaucratic obstacles to hiring the people that companies require to fill the gaps, on top of the unwelcome Immigration Skills Charge coming into effect later this year for non-EU workers. Small businesses in particular would be hit by such a cost," Marshall added.
British Hospitality Association chief executive Ufi Ibrahim agreed the plans were “very worrying”.
“The minister’s suggestion would increase the costs for hospitality and tourism businesses, in which four in five are SMEs and would lead to higher prices for consumers.”
And Institute of Directors head of employment and skills Seamus Nevin said that while firms agree that immigration policy will change, a £1,000 charge risks hitting the businesses that Britain needs to succeed after Brexit.
“Businesses are already working with ministers to improve the home-grown skills supply, but this tax will only damage jobs growth at a time when many businesses are living with uncertainty,” Nevin said.
“They simply cannot endure the double whammy of more restriction and then, if they do succeed in finding the right candidate, the prospect of an extra charge.”
Last year, home secretary Amber Rudd considered making British firms publish numbers of non-UK staff in a bid to “flush out” employers failing to make use of the local labour market.
London Chamber of Commerce and Industry policy director Sean McKee said the Home Office appeared to be seeking ways to penalise firms for recruiting non-British workers.
“The minister’s idea to impose a £1,000 a year levy on UK firms for each EU skilled worker they employ could potentially hamper and hinder UK firms as they strive to be successful,” Mckee said.
“With EU Nationals accounting for around 15% of the UK workforce that would be a lot of firms being effectively ‘fined’.”
Outside of the business world, the idea has also been condemnded by some of the government's political rivals.
Guy Verhofstadt, the European parliament's lead Brexit negotiator, was among the most prominent voices criticising the proposals.
Verhofstadt tweeted: “Imagine, just for a moment, what the UK headlines would be, if the EU proposed this for UK nationals?”
Similarly Open Britain, the campaign formed from the remnants of Britain Stronger in Europe, have branded the policy a a tax on succesful businesses.
Tory MP and Open Britain backer Anna Soubry said: ““Firms hire EU workers for the simple reason that we have skills shortages in this country. To get our own people into work, we need to focus more on training and apprenticeships.
"Stopping businesses from bringing in the workers they need will do nothing to help unemployed Brits, and will do everything to damage our economy.”