The Flyers, Pittsburgh, Minnesota, Detroit, and Chicago are believed to still be on Parise's list, and he hasn't ruled out returning to New Jersey.
In a text to reporter Mike Russo of the Minneapolis Star Tribune, Parise wrote, "[All I] can say is we made a lot of progress and we are closer today than yesterday."
"It's such a long-term, important decision, you have to make sure you look at everything," Parise told reporters in Toronto.
After word leaked that Parise was about to make a decision, Twitter exploded with comments and guesses.
About five minutes later, Parise cleared the air, saying he needed more time.
The Flyers reportedly have made 12-year offers for more than $80 million each to Parise and Suter, who are both 27. They are expected to receive, on average, $7 million to $8 million per season.
It seems their decisions will be based more on their comfort level with the city in which they play - and not on who offers the biggest contract.
Parise said the Devils' financial situation was not a factor.
Until Parise and Suter make their decisions, they are holding some teams hostage. Several teams are waiting to see whether they land one of the stars before they pursue other free agents or trades.
"We're just focused on the two free agents," one Flyers executive said when asked whether the team had made any headway in trade talks for Anaheim's Bobby Ryan or Columbus' Rick Nash.
The Flyers also are in the running for right winger Jaromir Jagr, 40, and defenseman Matt Carle, 27, two free agents they may re-sign.
If the Flyers do not land Parise, they could turn their attention to Phoenix's Shane Doan, a 6-foot-1, 223-pound right winger who scored 22 goals last season.
Doan, who will turn 36 just before the season, will not sign until July 9, by which time it should be known whether the Coyotes will stay in Phoenix. His first choice is to sign with Phoenix and spend his 17th season with the team.
Doan has scored at least 20 goals in 11 of the last 12 seasons.
As for Jagr, he reportedly is seeking $4 million per year after making $3.3 million last season, when he had 19 goals and 54 points.
Should the Flyers be unable to sign a marquee unrestricted free agent, would they turn their attention toward Shea Weber and give the star Nashville defenseman an offer sheet?
Highly unlikely, said someone familiar with the situation.
Weber is a restricted free agent, and Nashville would have the right to match the offer and retain him.
Trial on the Isle. Flyers prospects will participate in the annual "Trial on the Isle" competition, followed by a charity softball tournament, on July 11 in Stone Harbor, N.J. All proceeds will benefit Flyers Charities, with a donation going to American Legion Post No. 31.
The day will begin with a 9 a.m. swim in the ocean, followed by a run starting at the 96th Street beach to 123d Street. The prospects then will take part in team-building activities led by members of the military as they make their way back to the 96th Street beach.
At noon, Flyers prospects will host a clinic in the parking lot of Stone Harbor Elementary School at 275 93d St., and another clinic will be held at 3 p.m. at the 80th Street blacktop.
The prospects will be available to sign autographs at the school from 1:30 to 3:15 p.m. The admission fee is a $10 donation to Flyers Charities. Fans will receive a team photo of the prospects.
The prospects will play a charity softball game at 4 p.m. at the 80th Street field. At 5:30, a barbecue will be held at the Stone Harbor Yacht Club. Fans can make a reservation to have dinner with the prospects by calling 609-368-1201.
Contact Sam Carchidi at email@example.com, or follow @BroadStBull on Twitter.