Two of the contenders for the Labour leadership, Ed Balls and Diane Abbott, support full marriage equality.
Mr Balls, who was rated the most gay-friendly of the five candidates by Stonewall, has not made any statement on the issue but a member of his campaign team told left-wing blog Liberal Conspiracy that he was in favour of the change.
As a former minister, he is the most senior Labour figure yet to show his support for the change. While in power, the party’s line was that civil partnerships were sufficient.
However, Mr Balls was criticised while schools minister for a U-turn allowing faith schools to teach that homosexuality and gay marriage are wrong.
Ms Abbott, whose poor overall Commons attendance means she was absent for many gay equality votes, gave the website a statement saying she had “always supported gay marriage and made that case when civil partnerships were first discussed”.
Her spokeswoman told PinkNews.co.uk that she was in support of both civil partnerships and gay marriage.
The Miliband brothers, who have strong voting records on gay rights, have shown less support for the change.
David Miliband told PinkNews.co.uk last week that he did not have a “a closed mind ” on the issue but saw civil partnerships and marriage as equal.
In an interview with Liberal Conspiracy, Ed Miliband said: “I will listen to what people have to say on going further than that if there is a demand. No one has yet put that to me in the leadership election.”
He added that he felt not enough people wanted full marriage equality.
Andy Burnham, the fifth candidate, has the poorest gay voting record. His campaigns team had not returned a call for comment by the time of publication.
Civil partnerships, legalised in 2005, offer gay couples almost all the rights of marriage. Gay couples currently may not have a religious ceremony.
The UK’s largest gay organisation, Stonewall, has lobbied the government for religious civil partnerships but is not campaigning for them to be called marriage or for a change in the law.
However, other campaigners such as Peter Tatchell believe the law should be changed to reflect the respect given to the state of marriage.
The coalition government has said it supports giving churches the option of carrying out civil partnerships and senior figures such as David Cameron and Boris Johnson have made varying statements of their support for bolstering the recognition given to gay relationships.
Junior equality minister Lynne Featherstone told PinkNews.co.uk earlier this month that the government would consult relevant stakeholders on both gay marriage and religious civil partnerships.