Dr Fox, a standard-bearer for the Tory right, admitted there had been "muttering" about David Cameron's leadership but insisted the Prime Minister had silenced his critics over Europe.
Asked if he would take a post in the Government if Mr Cameron offered it, Dr Fox said anyone offered the chance to serve their country "ought to say yes".
Questions about Mr Cameron's leadership have been asked in recent weeks after reports backbencher Adam Afriyie was being touted as a successor.
Asked if Mr Afriyie was a "stalking horse" acting as cover for his own leadership challenge, the former Cabinet minister said: "I've been in Parliament for nearly 21 years and I can never remember a time in all 21 years when there wasn't muttering going on about whoever was the party leader at the time or prime minister at the time.
"The Prime Minister got a great victory for the UK at the EU summit this week, which of course all those defeatists said would not be possible."
Dr Fox quit the Government over his relationship with adviser Adam Werritty but indicated he would accept an offer of a return to the ministerial ranks from Mr Cameron.
He said: "That's not a question for me, that's a question for the Prime Minister and I'm sure he will have his view on that. If anyone was asked by a prime minister if you are willing to serve your country I think they ought to say yes."
He praised Mr Cameron's announcement that a Tory government would offer an in/out referendum on membership of the EU.
But he called for deeper reductions in public spending and tax cuts for businesses as he identified economic growth as the key factor if the Tories are to win the next election.
"We need to get a firmer grip on spending. One of the biggest rises in our budget is the interest we are paying on our debt. That has risen from just over £40 billion, it will rise to almost £60bn by the next General Election. That means we are paying more in debt interest than we are spending on defence and overseas aid and the foreign office all combined."
Contextual targeting label: