But the bloc insisted that it would have to be under EU rules and the European Court of Justice, a politically toxic condition in Britain give that national sovereignty was a key issue in the Brexit referendum.
"The European Council will monitor progress closely and determine when sufficient progress has been achieved to allow negotiations to proceed to the next phase on a future relationship", the draft guidelines say. But once there is a tentative consensus between the two sides on the reciprocal treatment of citizens in each other's nations, billions in budget commitments, legal clarity for companies working in Britain and a solution for Ireland's border with the United Kingdom, the European Union says it would be willing to look ahead. He signaled that Britain would only be able to commence talks on the future relationship once there was "sufficient progress on the withdrawal".
Mr Tusk hopes that "significant progress" will be made by autumn of this year, but that seems to depend on London accepting Brussels' calculation of how much it owes.
Mrs May formally notified the European Union of Britain's intention to leave in a letter to Mr Tusk that diplomats described as surprisingly conciliatory in tone for the most part.
Mr Johnson, the Foreign Secretary, led discussions by saying that Britain had a "strong hand" at the negotiating table when it came to security, the paper reports.
"Starting parallel talks on all issues at the same time as suggested by some in the United Kingdom will not happen", the former Polish premier said.
European Union leaders have warned that the two years of talks triggered this week to negotiate Britain's exit will be hard - but insisted they don't want all-out economic or diplomatic conflict.
These include the timeframe for wrapping up the EU-U.K. talks, which remains unclear but has been an early sticking point ahead of negotiations.
The challenges prior to moving onto the next step of talks are sizable, however. Populist voices in Britain have urged the Conservative government not to pay a penny.
The tiny British overseas territory on Spain's southern tip has always been the subject of an acrimonious sovereignty row between London and Madrid, which wants Gibraltar back after it was ceded to Britain in 1713.
"After the United Kingdom leaves the Union, no agreement between the EU and the United Kingdom may apply to the territory of Gibraltar without the agreement between the Kingdom of Spain and the United Kingdom", the draft says.
But Timmermans said: "You can't blackmail someone with one of your own existential requirements. there is no real possibility for blackmail there because security for the United Kingdom, even if they're not in the European Union, will stay an essential requirement for themselves".
However, Europe would not adopt a punitive approach as "Brexit in itself is already punitive enough".
European Council President Donald Tusk (L) speaks at a joint press conference with Maltese Prime Minister Joseph Muscat (R) in Valletta, Malta, on March 31, 2017.
Tusk also ruled out the suggestion that there was an inherent threat in May's departure letter Wednesday, which some felt hinted that Britain would end its security cooperation with continental Europe unless it gets a good Brexit deal.
'I know Theresa well enough and I know her approach to this issue.
Boris Johnson said: "I want to stress one thing, the UK's commitment to the defence and security of this region, of Europe, is unconditional and it is not some bargaining chip".
It is clear the United Kingdom will face a tough divorce, the BBC's Gavin Hewitt says, but there were some hints at flexibility from Mr Tusk.
British foreign secretary Boris Johnson, in Brussels as North Atlantic Treaty Organisation ministers met U.S. secretary of state Rex Tillerson, said London was committed to European security and that it was "not some bargaining chip" in the Brexit talks. The EU will also work to avoid a legal vacuum, and push to ensure Britain honoured all its "financial commitments" taken as a member state. "There's a lot of good will, willingness to achieve what the Prime Minister has said she wants to achieve", he said. On Thursday, U.K. Prime Minister Theresa May revealed plans addressing how European Union laws will be converted to domestic code-that includes the 12,000 European Union regulations British citizens now follow.