Heyman added that while many involved with the Phillies "love" Arrieta due to their familiarity with him dating back to his time with the Baltimore Orioles, they would rather sign him to a shorter-term deal than he is seeking.
Arrieta is among the biggest names remaining in a free-agent market that has taken longer than usual to clear out.
Spring training is already underway, but Arrieta would provide a major boost to Philadelphia's rotation even if he starts off slightly behind the rest of his teammates in terms of preparation.
The 31-year-old righty is a one-time All-Star who is coming off a spectacular, four-year stretch with the Chicago Cubs.
During his time with the Cubs, Arrieta went 68-31 with a 2.73 ERA and one National League Cy Young Award. He was also key in Chicago ending its Word Series championship drought in 2016 as he went 2-0 in two Fall Classic starts.
Arrieta struggled at times last season, but he bounced back in the second half and finished with a 14-10 mark to go along with a 3.53 ERA and 163 strikeouts in 168.1 innings pitched.
The Phillies are coming off a 66-96 season, and they haven't reached the playoffs since 2011.
Philadelphia has some good, young talent throughout its roster, however, and signing Arrieta would give it a dynamic duo atop its rotation along with Aaron Nola.
The Washington Nationals are still the class of the NL East, but signing Arrieta could go a long way toward getting the Phillies in the mix ahead of the New York Mets, Atlanta Braves and Miami Marlins.