The 27-year-old, who earned $3.47 million this season, is expected to command close to $5 million as one of the most steady and underrated blueliners available this summer.
While Holmgren hopes to have Carle return to Philadelphia, the defenseman is likely to field offers from several teams.
"I think Matt had a good year," Holmgren told the Daily News. "He's up there in numbers and Matt's a good defenseman. I've said that before, if Matt wants to be here, we'd like to have him back."
The Flyers could find it beneficial to invest in Carle, as the team's defensive corps needs some shoring up with captain Chris Pronger's status still unknown for next season.
"I don't see any reason why we can't work out a deal," Holmgren added. "His demands, when I spoke with him and his agent, nothing was ever out of line. Could we get him under market value? I would say that we probably could. I don't see any issues there."
In 82 games with the Flyers this season, Carle tallied four goals and 34 assists for 38 points, while posting two goals and four assists for six points in 11 playoff games.