At a security summit in Brussels, she has had lunch with Angela Merkel and will later meet the EU's Donald Tusk,
The PM has been told she has until the start of December to make an enhanced offer on money and the Irish border.
Ministers have given her their backing to increase the UK's "divorce bill" but only if the EU shows movement on trade.
Arriving in Brussels, the prime minister said both sides "must step forward together".
Environment Secretary Michael Gove refused to confirm or deny reports that the government had agreed to pay about £40bn to pave the way for EU leaders to approve the next phase of talks at a summit on 14 December.
The British prime minister will later meet Mr Tusk, who as European Council president represents the 27 other member states, on the margins of a summit on security threats in Eastern Europe.
Asked whether she was prepared to offer a "blank cheque" to the EU to get what the UK wants, Mrs May signalled the onus was on the EU as well as the UK to make progress.
"These negotiations are continuing but what I am clear about is that we must step forward together," she said. "This is for both the UK and the EU to move onto the next stage."
Last week Mr Tusk said the EU was "ready" to move onto the next phase of Brexit talks but the UK must first show more progress on the outstanding issues.
'Exemplary'
Mr Gove, who was one of those ministers reported to have sanctioned the higher offer at a meeting of a key Brexit committee earlier this week, hit out at the "assumptions" and "assertions" reported in the media.
"I am not going to reveal what happened in a cabinet sub-committee.
"I am not going to provide a commentary on the negotiating stance because the PM and David Davis should be free to get the best deal for Britain."
The PM, he added, was handling the negotiations in an "exemplary fashion", saying he was confident that she would "put the national interest first" at all times.
The UK voted to leave the EU in June 2016, and served the EU with formal notice of Brexit in March 2017. This began a two-year countdown to the UK's departure day which will be in March 2019.
During Friday's meeting, Mrs May will also warn EU leaders to be wary of "hostile states like Russia" and pledge the UK will stay committed to European security after Brexit.
"We must be open-eyed about the actions of hostile states like Russia who threaten the potential growth of the Eastern neighbourhood and try and tear our collective strength apart," she said.
She is expected to use the summit to demonstrate that the UK can contribute to European security after Brexit, for example by spending £100m over five years to fight Russian disinformation campaigns.
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