Some teams on the West Coast are also expressing interest, Murray adds.
The Braves already have catcher Travis d'Arnaud, who accrued a .919 OPS with nine homers in 44 games last season. However, he has one year left on his contract and has dealt with injuries in the past.
The two-time All-Star amassed a .825 OPS with 36 homers over his two years with the Phillies.
The Toronto Blue Jays and Washington Nationals have also been linked to Realmuto during the offseason. However, it's not known if the Blue Jays are still looking at signing the backstop after reportedly adding George Springer to a lucrative multi-year deal Tuesday.