Mr Tusk's offer has left Prime Minister Theresa May reeling and facing awkward questions as well as substantial pressure to "bite Tusk's hand off" just days after calling on Tory Brexiteers to come together.
The Wall Street investment bank said the business, previously run via Citibank Europe plc, headquartered in Ireland, would be transferred to the new bank by March 2019 subject to approvals from regulators.
Negotiations faltered after the European Union said last month that British Prime Minister Theresa May's proposal for post-Brexit economic relations was unacceptable.
But there is still no agreement on some issues, including how to avoid new checks on the Irish border.More news: Mark Lawrenson states his prediction for Liverpool FC v Man City
Tusk said the European Union remained "united behind Ireland" and the need to "preserve the Northern Ireland peace process".
Mr Tusk, a former prime minister of Poland who was held prisoner as a young man living behind the Iron Curtain, made a clear reference to Mr Hunt's remarks after meeting Irish premier Leo Varadkar in Brussels.
"Our will is unbroken to reach agreement with the British government", he said.
Any such compromise would leave the European Union concerned that Britain could use Northern Ireland's special access to the bloc's single market to sell cheaper goods that would not adhere to European Union labour, environment and other standards. People are anxious about their future, their future prosperity, their jobs, the economy.
That, in turn, is a hard one for Britain where Prime Minister Theresa May's government relies on the support of the Northern Irish Democratic Unionist Party, which vehemently opposes differing rules on its soil from the rest of the United Kingdom.More news: Nobel Peace Prize awarded for efforts to end sexual violence in war
But in the event that no deal is reached by the Brexit deadline, both sides agree there needs to be a "backstop" solution - which means a last resort plan - that would keep the Irish border open.
Negotiations between London and Brussels have reached an impasse due to uncertainty over the future of the Irish border.
"The EU is serious about getting the best possible deal", he said.
There is no official confirmation of the plans or when the proposals will be presented to the European Union, she added.
BBC political editor Laura Kuenssberg said United Kingdom officials were understood to be working on plans for a "hybrid backstop" with light-touch regulatory checks between Great Britain and Northern Ireland, the possibility of some kind of democratic oversight from Stormont and a temporary extension of the customs union to the whole of the United Kingdom in the event that a free trade deal has not been completed.More news: India vs West Indies 1st Test, Day 2