Dutchman Timmermans also rejected claims by British finance minister Philip Hammond that the EU was pushing a punitive deal for Britain because it was paranoid that other countries would leave.
"Tell us what you want. That would be useful," Timmermans, the right-hand man to European Commission chief Jean-Claude Juncker, told a small group of Brussels-based media including AFP.
"We are not leaving the UK, the UK is leaving the EU. So tell us what you want," Timmermans added.
"We need to know precisely what the UK wants and then we will negotiate."
A year and a half after Britain's shock referendum vote to leave the EU, Prime Minister Theresa May has still not set out what kind of relationship she wants with the bloc after Brexit.
Discussions on future relations -- including the all-important issue of a possible trade deal, and how closely Britain will stay allied to the EU's single market and customs union -- are not due to start until April.
Hammond told Welt Am Sonntag in Germany that Britain's economy should maintain a "European approach" after Brexit, hinting at a minimum of economic divergence with the EU.
But Hammond also warned the EU against the "paranoia" of thinking that going too soft on Britain would give an incentive for the other 27 countries to leave.
Timmermans said elections in the Netherlands and France, where eurosceptic candidates lost out, showed that the fallout from the Brexit vote had in fact discouraged others from following suit.
"So the trend is not towards EU leaders being afraid that this might have a sort of ripple effect or lead to temptations of others doing the same. On the contrary I would say," he added.
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