Twitter user Alexis Isabel Moncada was the first to bring up the idea on Saturday, tweeting, "I hope Disney makes Elsa a lesbian princess imagine how iconic that would be."
Her follow up tweet, "Dear @Disney, #GiveElsaAGirlfriend," has been retweeted more than 1,700 times.
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Moncada explained her petition in an article posted to MTV.com, saying, "The entertainment industry has given us girls who have fallen in love with beasts, ogres who fall for humans, and even grown women who love bees. But we've never been able to see the purity in a queer relationship."
She added that "many in the LGBT community view Frozen as a metaphor for the experience of coming out and accepting who you are. Yet Elsa, the film's protagonist, will probably end up with a male prince or king in the upcoming Frozen sequel."
One Twitter user wrote, "Love is an open door. That door should be open to everyone, not just straight people. #GiveElsaAGirlfriend."
Another agreed, "#GiveElsaAGirlfriend positive queer role model are needed from a young age; early exposure leads to better understanding/acceptance."
Frozen 2, which is currently in production, is slated to be released before 2018.