Heyman added that while the Philadelphia Phillies and Milwaukee Brewers have an "outside chance," talks between the O's and Dodgers are heading "toward the finish line."
The 26-year-old Machado is in the midst of his best season, hitting .315 with 24 home runs and 65 RBI.
The four-time All-Star is on pace for career highs in most major offensive categories, which makes him one of the most highly sought after deadline rentals in recent memory.
Since Machado can become a free agent during the offseason, the team that trades for him will be taking a huge risk in terms of giving up assets in return for what may only be a few months of Machado's services.
It may be a worthwhile move for a team like the Dodgers since they hold a half-game lead over the Arizona Diamondbacks for first place in the NL West.
The National League is weak in comparison to the American League, which means the door is open for several teams to potentially make a deep run.
Considering the Phillies and Brewers are also in playoff positions currently, acquiring Machado would not only help the Dodgers, but it would also prevent some of their closest competitors from getting better.
Acquiring Machado would likely kick Chris Taylor back to the outfield, giving the Dodgers one of Major League Baseball's most potent infields, as it also includes Cody Bellinger, Max Muncy and Justin Turner.
L.A. has a deep and talented farm system, and although it is unclear who it would need to part with in order to land Machado, MLB.com lists outfielder Alex Verdugo, catcher Keibert Ruiz, pitcher Mitchell White, outfielder Yusniel Diaz and pitcher Dennis Santana as some of the Dodgers' top prospects.
The Dodgers have been on a roll since some early-season struggles, and while they are a respectable ninth in the league in runs scored and fifth in home runs, Machado would both elevate their offensive potency and likely make them the team to beat in the NL if they aren't already.