They "are seeing each other and very into it," the insider told the celebrity news Web site. "Their kids have met and everything. It's getting very serious."
However, Braxton's publicist is downplaying the romance report, stating, "Toni and Eddie are just friends and have been fans of each other's work for a long time."
Murphy has eight children from previous relationships.
Braxton was married to musician Keri Lewis from 2001 to 2009. They have two children together.
2014: The Year in Music [PHOTOS]