Deputy Prime Minister Mr Clegg said people would judge a potential prime minister on their ability to lead rather than if they were gay, as he insisted he would have no issues at all if "one of my boys told me that he liked another boy".
And Labour leader Ed Miliband expects there to be a gay PM in the future as social attitudes have driven a series of changes, including equal marriage, in the last 20 years.
Prime Minister David Cameron also said "sexual orientation should be neither here nor there" as people are helped to achieve their full potential - including becoming PM.
He added that more role models - either straight or gay - were needed to encourage best behaviour in sport, adding clubs "must tackle problems on the terraces".
Mr Clegg and Mr Miliband were responding to questions from Gay Times (GT) readers while Mr Cameron wrote an open letter for the latest edition of the publication, which is available digitally today and in print next Wednesday.
On whether the public would accept a gay PM, Liberal Democrat Mr Clegg told GT magazine: "Yes and why not?
"Being gay doesn't affect how you work, how you interact with people or how you make decisions. I'm confident that the British people would judge him or her on their ability to lead and be a good prime minister and not on who they choose to share their life with."
Asked if he could foresee a gay PM, Mr Miliband said: "Yes. I think the world has changed a lot.
"If you think about the way the world has changed in the last 20 years since I was at college we've seen the repeal of Section 28, we've seen civil partnerships, the lowering of the age of consent, equal marriage and that has been driven by change in social attitudes and that is why I think absolutely it's foreseeable to have a gay prime minister."
Mr Clegg said he hoped in the future children would not dread coming out to their parents.
Asked how he would react if one of his children was gay, Mr Clegg answered: "I would have no issues at all if one of my boys told me that he liked another boy.
"It's not a choice, it's who you are and I would love my boys regardless of their sexuality. I just hope that some day coming out to your parents is not going to be something you dread but something you will remember fondly."
Mr Miliband added on the same issue: "I would love them equally as much. The most important thing to me is that my kids are happy and I don't care whether they're gay or straight. That's what matters to me."
In his open letter, Mr Cameron said he was proud to be PM of a country judged to be the "best place to live in Europe if you are lesbian, gay, bisexual or trans(gender)", adding the Government was attempting to fight prejudice where it remains.
On sport, the Conservative went on: "We are working to break down barriers in sport, too. People should be able to excel in sport regardless of their sexuality - but we know how hard it's been.
"We have seen the enormously positive reaction to people like Thomas Hitzlsperger and Gareth Thomas being open about their sexuality, and hopefully that will encourage others to be more open too.
"But we need more role models, straight and gay, to encourage the best behaviour and clubs must tackle problems on the terraces."
UK Independence Party leader Nigel Farage was also invited to write an article for the magazine, in which he was asked if his party would pledge to expel homophobic members in the future.
He told GT magazine: "It would sound great to say, 'yes, we would expel anybody who was a homophobe', but how would that be judged, or investigated or enforced? Are there limits to what is acceptable and unacceptable, in terms of political correctness? Who is the ultimate arbiter of morality or taste?
"Even within one section or group of society there will be very different notions of what is fine and what is deemed insulting or upsetting. We are a political party, not the thought police, and never would we wish to become anything different."