The Gossip Girl alum, 33, and the Deadpool star, 44, who share daughters James, 6, Inez, 4, and 16-month-old Betty, have donated millions of dollars to organizations working to protect the rights of immigrant children separated from their families and awaiting deportation.
"Day by day, they've been warming up to the idea of providing an orphan with a forever home," shares the source, who notes the idea of expanding their brood is nothing new.
"Ryan jokes that Blake's a baby machine who would have no trouble getting pregnant again. But their hearts really go out to these kids. Blake and Ryan live a blessed life and feel like they've got so much more to give!
"Motherhood is what fulfills Blake the most," says a source, adding that Ryan is "fully committed" to the idea of adding a fourth child to their crew.
An OK! previously reported, Lively, who's revealed she would happily "spit out a litter of kids," is "really yearning for one more." Last year, a source told OK!, "She loves being pregnant — and Ryan's always joked that he'd like another daughter to complete his tribe of Amazon women!"
Whether by adoption or pregnancy, it was reported that the Lively and Reynolds "are pulling out all the stops to make it happen," and that expanding the family had become one of the top priorities for the couple.
"Blake's doing maybe one movie a year, but being a mom is what fulfills her. She's never had a problem getting pregnant before, so they expect to have some happy news for their families" sometime soon, the source added.
Lively and Reynolds got married in September 2012. More recently, they have been enjoying time together quarantining amid the ongoing COVID-19 pandemic.