Its current definition says marriage is "intended to be a permanent relationship between a man and a woman..."
At the annual meeting of its Conference at Westminster Central Hall in London, the Methodist Church's Marriage and Relationships Task Group presented the findings of a two-year consultation on the issue.
Setting out his conclusions from the report which involved more than 8,000 people, chair Revd Graham Carter said there was "a clear mandate" to "revisit" the Church's definition of marriage through "a theological re-examination."
In his report, Revd Graham Carter stressed 'revisiting' the Methodist Church's definition of same-sex marriage would "potentially create an opportunity to reconcile the Church with those it has already lost" and did not necessarily equate to changing its stance.
He added: "The current situation leaves many same-sex couples within the church, and most same-sex couples outside the church, and their families and friends, continuing to feel alientated, unloved and unaccepted by the Methodist Church."
Demonstrating division within the Methodist Church over the issue, representatives at the Conference heard views both for and against the possibility of the Church's definition of marriage being changed.
Revd Graham Carter's report said there is some concern within the Methodist Church that opting into same-sex marriage "could damage its prophetic and counter-cultural role by giving into changes in society" and he emphasised the Bible should form the context for future discussions.
A two-year task group will now explore how this process takes shape, before it reports back to the 2018 Conference.
The fourth-largest Christian denomination in the UK, the Methodist Church in Britain has 202,000 "committed" Methodists but it reported a "significant" drop it's membership between 2004 and 2014.