A proposal to permit ministers and deacons to carry out the ceremonies will be debated when the Church holds its annual General Assembly next month.
The General Assembly will scrutinise a report by the Church of Scotland's Theological Forum which concluded that it "does not believe there are sufficient theological grounds to deny nominated individual ministers and deacons the authority to preside at same-sex marriages."
A controversial decision was made in 2009 to appoint gay ministers in Scotland, while ministers have been allowed to be in same-sex marriages since last year.
Welcoming the Theological Forum's conclusion, the first openly gay Church of Scotland minister, Rev Scott Rennie, told Premier: "I think it's a positive step. I think it's a positive step in the Church's thinking.
"We have been on a road towards inclusion of gay people, now, for the best part of ten years so I see it simply as the next step on that journey."
Gay marriage has been legal in Scotland since 2014; however, the Church of Scotland is protected under equalities legislation from having to conduct such ceremonies.
Opponents fear a step towards allowing ministers to conduct same-sex marriage would be a step away from Biblical teaching.
Rev Rennie added: "We ought to be encouraging people to live in committed relationships, relationships that reflect the love Christ has for his people.
"So, I found it difficult to understand arguments against marriage on the grounds of sexuality."
The Theological Forum also urges the Church of Scotland to apologise for its "history of discrimination".