Financial terms were not disclosed, but sources told TSN of Canada the deal would be worth $1.9 million for one season.
The Vancouver Canucks have seven days to match the offer or accept the Flyers' second-round pick in the 2007 draft. Canucks GM Dave Nonis has refused to comment, but sources told TSN that it is an absolute certainty Vancouver will match the offer sheet.
A restricted free agent, Kesler scored 10 goals and 23 points in 82 games with the Canucks last season, his first full campaign in the NHL.
Vancouver's first-round pick in 2003, the 22-year-old Kesler has 12 goals and 16 assists in 110 career games with the Canucks.
Information from SportsTicker was used in this report.