The Flyers acquired Hayes in a trade with the Winnipeg Jets on June 3 for a fifth-round pick in the 2019 NHL Draft. The first round is June 21 (8 p.m. ET; NBCSN, SN, TVAS). Rounds 2-7 are June 22 (1 p.m. ET; NHLN, SN).
"Certainly, we will have a lot more dialogue this week," Flyers general manager Chuck Fletcher said Monday. "Next week is the week of the draft. This week will be an important week. I will certainly have more time to meet with him face to face.
"Had some good, I guess, preliminary conversations with Kevin and his representation. I expect to follow up with Kevin and his camp this week and we will see how it goes. I don't know how to characterize it other than we've had good conversation and we are hopeful we can make something work.
"I don't have a vibe, other than he's certainly open-minded. You have to remember he's two weeks away from getting to July 1, so that's a nice status to obtain in this league. Certainly, he's earned that right and we are respectful of that. I think we have a lot to offer in Philly. So we will continue to speak to him and I think he's open-minded to conversations, at least that is what his camp has said to us, and obviously we have strong interest in him."
Hayes had 55 points (19 goals, 36 assists) in 71 games with the Jets and New York Rangers this season. New York traded him to Winnipeg for forward Brendan Lemieux and two draft picks on Feb. 25.
Hayes could slot in as Philadelphia's second-line center, which would allow Claude Giroux to remain on the wing full time after playing both spots last season, and Nolan Patrick to have easier matchups as a third-line center. Hayes also could play on the power play and the penalty kill.