CSN reported that both were offered 12-year deals for more than $80 million apiece.
Parise also fielded offers from Pittsburgh (the favorite), Minnesota, Carolina, Detroit, and Los Angeles, among others. Parise said he hasn't ruled out returning to New Jersey.
Suter also received numerous offers.
The Flyers also made an offer to get unrestricted free-agent defenseman Matt Carle back in the fold. Carle may be waiting for Suter to decide before he makes a decision. Once Suter signs, Carle will move higher on some teams' lists.
Late Sunday, Carle's agent, Kurt Overhardt, said that he was considering "several offers" and that there wasn't a timetable for signing.
The Flyers want to re-sign 40-year-old Jaromir Jagr, but the right winger's agent was considering several offers Sunday night. Jagr's asking price may have increased after Ray Whitney, 40, who had 77 points with Phoenix last season, signed a two-year deal with Dallas for $4.5 million per season. Jagr earned $3.3 million last season and had 19 goals and 54 points.
The trade market includes gifted wingers Bobby Ryan of Anaheim and Rick Nash of Columbus. Teams' interest in those stars figures to increase after Parise signs.