However, the team's front office also likes veteran skipper Buck Showalter, according to Heyman.
Girardi, 55, is in Philadelphia on Monday for a second meeting with the team and is the "clear favorite for that job," David Kaplan of ESPN reports.
The rumored three finalists for the Phillies' managerial vacancy are Girardi, Showalter, and Dusty Baker.
The New York Mets are looking to fill the same position, and Girardi is reportedly one of their final candidates, along with Carlos Beltran, Eduardo Perez, and Tim Bogar.
Girardi owns a 988-794 career record and managed the New York Yankees to a World Series win over the Phillies in 2009. He stepped down as the skipper of USA Baseball on Oct. 16 to pursue a major-league job.
Philadelphia fired Gabe Kapler on Oct. 10 after two seasons as the club's manager.