The Canucks are interested in Flyers forwards Brayden Schenn and Sean Couturier, and want one of them included in a deal for Kesler.
Canucks GM Mike Gillis is also interested in prospects Scott Laughton and Samuel Morin.
Kesler, who has a no-trade clause, is willing to accept a trade to the Flyers, as well as the Pittsburgh Penguins and Detroit Red Wings, both of whom have also inquired about his availability.
The Chicago Blackhawks and Los Angeles Kings also expressed interest in Kesler, but the Canucks will not deal him to either team, while the Toronto Maple Leafs and Columbus Blue Jackets have been told Kesler will not waive his no-trade clause to go there.
Late Monday night, the Pittsburgh Tribune-Review reported the Penguins have offered center Brandon Sutter, a pick of young defensemen Simon Despres or Brian Dumoulin, a 2014 first-round draft pick and a 2014 third-round pick in exchange for Kesler.
Penguins GM Ray Shero is willing to up his offer, if need be.
Flyers GM Paul Holmgren has also discussed Canucks defenseman Alexander Edler, who has a no-trade clause.