David Cameron insisted he is "confident" the UK will remain in a reformed European Union if he gets the deal he is seeking for a new relationship with Brussels.
The Prime Minister said he is in "no hurry" to secure a deal on a package of reforms to Britain's EU membership at the upcoming Brussels summit in February but if an agreement is reached he will "sell it very hard" to the public ahead of the promised referendum.
A deal at the European Council of February 18-19 is widely seen as essential if Mr Cameron is to stage his in/out referendum before the summer.
Mr Cameron told ITV News: "A deal could be done in February, there is progress in each of the four areas I have identified and with goodwill I think we could get that deal.
"What I am saying very clearly is if there is a deal on the table, there will be no funny business from me, I will pick it up, I will take it to the British people and I will sell it very hard because it will be right for Britain.
"But if it isn't ready in February, if it isn't what I want, if it isn't what I want, if it isn't what is right for Britain, then we will need to take more time. Getting this right is more important than getting on with it."
In an interview with French broadcaster TF1 he denied his reform demands were an attempt to "blackmail" fellow EU leaders into agreeing to reforms instead of risking a British exit.
"No, I don't believe it is. I mean, we have raised the concerns we have over many years, and I set them out very clearly in my manifesto that I put in front of the British people. And I don't think the things we're asking for are unreasonable."
He acknowledged the referendum was a "huge responsibility" but "I think now, asking the British people to stay in a reformed Europe or leave, it's the right time to do that, particularly if we can achieve these changes on competitiveness, on political union, on the euro, on migration".
"If we achieve these things, then I'm confident we'll stay in a reformed Europe," he added.
Asked if he felt "deeply European", the Prime Minister replied: "Of course. Britain is a European country, and I feel very much part of that."
The Prime Minister was interviewed in Davos on the latest stage of his diplomatic offensive to build support for his reform demands before heading to Prague for talks on Friday.
In his speech at the World Economic Forum event he said he was ready to be "patient" in order to get the right result.
Securing a deal next month was "achievable (and) doable", he said. But he added: "We are certainly not there yet."
Britain's demands for change on the four issues of migration, sovereignty, competitiveness and protection for non-euro states were "not outrageous asks", but offered "a huge prize", he said.
Prospects for a swift agreement were played down by French prime minister Manuel Valls, who said the negotiations had "only just begun" and warned that a deal "at any price" would not be acceptable.
Mr Cameron held talks with Mr Valls at the Swiss ski resort, along with Dutch prime minister Mark Rutte and his counterpart from Luxembourg Xavier Bettel.
A Downing Street spokeswoman said: "In all three the PM discussed the UK's renegotiation of its membership of the EU. Everyone agreed the importance of maintaining momentum towards getting a deal done, noting that there was a good understanding of the main issues and that with hard work solutions could be found in all four areas."
Sweden's migration minister Morgan Johansson told Channel 4 News: "I think that the Prime Minister is playing a game with quite high stakes here.
"We will see where it ends up but I hope the UK will still be a part of the European Union."