The Conservatives and DUP are now still continuing talks in order to secure a deal, although reportedly only minor details remain to be ironed out.
A Conservative source said there was so far no deal to announce and that a decision on the timing of any announcement would have to wait until an agreement was finalised. The price of such a deal remains unclear.
A DUP source said: "Our discussions are continuing".
Labour leader Jeremy Corbyn has said Labour stands ready to vote down the Queen's Speech, which sets out the government's legislative agenda, underlining the need for Mrs May to secure DUP support from the outset of the new parliament.
Sir John spoke to just before the leader of the DUP party, Arlene Foster arrived at Number 10 Downing Street.
"She doesn't have a mandate for scrapping the winter fuel allowance, or taking hot meals away from children, and there could be support for other things too, such as scrapping the bedroom tax", the source said.
Schaeuble said in a televised Bloomberg interview that Hammond had relayed that the party is now trying to work out what it means that "a lot of young voters voted for Labour, not for the Conservative Party".
"The power-sharing institutions collapsed because of the DUP's RHI financial scandal and the refusal of previous Tory governments and the DUP to implement previous agreements".More news: For Labour's Corbyn, strong result turns defeat into victory
He added: "The Brexit process will not be like a member leaving a club of which he or she no longer wishes to be a member, which is an easy enough process, once the bar bill has been settled".
While the DUP is deeply euroskeptic, they have balked at some of the practical implications of a so-call hard Brexit - including a potential loss of a "frictionless border" with the Republic of Ireland - and talks will touch on efforts to minimize the potential damage to Northern Ireland.
The Alliance Party has warned that the talks process is bereft of "impetus and momentum".
"My clear view, and I believe the view of the majority of people in Britain, is that we should prioritise protecting jobs, protecting economic growth, protecting prosperity as we enter those negotiations and take them forward", Hammond said."As we enter negotiations next week, we will do so in a spirit of cooperation, taking a pragmatic approach, trying to find a solution that works both for the United Kingdom and the European Union 27", he told reporters before a meeting of the 28 EU finance ministers in Luxembourg.
He urged ministers to make jobs and the economy their priority in negotiations.
"We have been very clear that we want to maintain a close relationship and a close partnership with the European Union and individual member states in the future", May said at a joint press conference.
But in a statement, officials said: "David Davis, Secretary of State for Exiting the European Union, and Michel Barnier, the European Commission's chief negotiator, agreed today to launch Article 50 negotiations on Monday, June 19".
Referring to speculation that negotiations could be extended until March 2019, Barnier said: "If we work seriously, I see neither the usefulness nor the interest of pushing back this date".
But after a generation of discord over Europe inside her party, May's future could depend on her ability to please both the eurosceptic and pro-European factions in her party.