Many potential successors inside and outside her cabinet will address delegates this week, notably Johnson, who quit in July over May's Brexit plan.
The former Attorney-General, who serves as the ad hoc leader of a group of European Union loyalist rebels which has already voted against the Government to defeat aspects of the legislation to deliver Brexit in Parliament, declared that "the time has come for a polite rebellion by pragmatic Conservatives" in a Sunday Telegraph article.
Asked by the Daily Mail whether Mr Johnson could become prime minister, Mr Hammond said "I don't expect it to happen" and suggested Mr Johnson could not do "grown-up politics".
In his interview with the Sunday Times, he made a direct pitch for the leadership by setting out a slew of domestic policy ideas.
"What Chequers does is offer an in-the-middle solution, down the center, taking the best from both models, and proposing a way forward which delivers on the mandate of the British people in the referendum but also protects British jobs and British businesses", he told Sky News.
"It isn't just about making flamboyant statements and big announcements, it's about getting things done".
Former foreign minister Johnson, long tipped as a successor to May, used a newspaper interview to condemn her plan for close economic ties with the European Union as "deranged" and "preposterous".
"The mood is undoubtedly that people want to do a deal with the UK", Hammond told the BBC on Monday.
French singer Charles Aznavour dies aged 94: spokeswoman
The famed French singer Charles Aznavour , known colloquially as the "French Frank Sinatra", has died aged 94. News of the singer's death generated an outpouring of grief and gratitude.
PM Theresa May's plan to host a post-Brexit "Britain" festival has been gaining traction online since it was announced Saturday. He told Radio 5 Live he was "not having sleepless nights" over the risk of a no-deal Brexit.
"Clearly there has been a hit to the economy through the uncertainty the Brexit process has caused". "I believe when the prime minister lands this deal and brings it back there will actually be a boost to the economy".
"Many businesses are sitting on their hands frankly waiting to see what the out turn of this negotiation is before confirming their investment plans", he said.
Foreign Secretary Jeremy Hunt used a Telegraph interview to warn Brussels it would stir up a "Dunkirk Spirit" if it forced Mrs May into a bad deal.
"We've had our arguments, but now is the time to put them behind us, now is the time to come together, because this is a moment for the optimists", he said.
Britain's Brexit chief appealed for Conservative Party unity on Monday, as he warned the European Union that the United Kingdom will leave the bloc without a divorce deal rather than accept one that makes Britain follow too many EU rules.
"The prime minister was very clear and very honest with the public that if we want in the future a growing NHS to support our aging population of course we'll have to accept a little more tax to fund that service", he said.