Everyone in the current Conservative Cabinet is a Eurosceptic, Defence Secretary Michael Fallon says.
Mr Fallon said there were no "Euro-fanatics" around David Cameron's top table, adding that everyone was behind the PM's bid to reform the EU.
He dismissed newspaper reports that potential rebels who might criticise the result of his renegotiations would be reshuffled.
A referendum on the UK's membership of the EU will be held by the end of 2017.
Beforehand, Mr Cameron has pledged to win back powers from Brussels and says he wants to campaign to remain in a reformed EU.
The prime minister said for the first time on Thursday that he would be publishing a list of the specific reforms in early November he is seeking, after calls for clarity about his demands.
Campaigners to leave the EU predict the demands will be "marginal", and Eurosceptics have said some ministers will resign unless they are allowed to campaign to leave.
Staying or going?
- David Cameron has promised a nationwide referendum on the UK's membership of the EU by the end of 2017
- The likely question is: "Should the United Kingdom remain a member of the European Union or leave the European Union?"
- The prime minister has promised to renegotiate the UK's relationship with the EU beforehand, and says he wants the UK to stay in a reformed union
- Campaigns have recently been launched on both sides of the argument
The Sunday Times claimed Mr Cameron was being urged to "sack his critics instead", but this was rejected by Mr Fallon during an appearance on The Andrew Marr show.
"I don't know where you get this stuff", he said.
Mr Fallon added: "We're all Eurosceptics now. I don't see any Euro-fanatics around the Cabinet table."
Ministers are "all firmly behind the prime minister" in his attempts to get a "better deal", he added.
Mr Fallon said the movement of people and the claiming of welfare would be "one of the key areas where we need to see reform".
'Two to tango'
However, other EU leaders have warned Mr Cameron the principle of free movement is "non-negotiable".
Mr Cameron's reform demands, which are also likely to include exemption from an "ever-closer union" and safeguards for non-eurozone countries, will be revealed in a letter to European Council President Donald Tusk.
The prime minister has promised to "quicken the pace" of negotiations after European Commission President Jean-Claude Juncker said on Wednesday that "huge progress" was not being made and reminded the UK that "it takes two to tango".
His requests are likely to be considered by his counterparts at the December meeting of the European Council.