If either does not sign with the Predators by July 1, he can receive an offer sheet from another NHL team that Nashville can match.
Poile also said he has spoken with Vegas Golden Knights general manager George McPhee about the NHL Expansion Draft. Poile said he believes Nashvile will be losing one of the better players Vegas selects, and he said he's hoping he can work out something to allow the Predators to protect as many assets as possible.
The Predators are expected to protect four defensemen (Roman Josi, P.K. Subban, Mattias Ekholm and Ryan Ellis), which means they can protect four forwards (Arvidsson, Johansen, Forsberg and likely either James Neal or Calle Jarnkrok).
"It's going to be tough," Poile said. "Whatever we do, I think we're one of the teams that is going to give up one of the better players in expansion. I've also made a call, talked to George McPhee [on Monday], and I'm going to talk to him again [Thursday] just to see if I can see what he might be looking for and see whether there might be a deal that we could make that we could make to satisfy both of us.
"It's the cost of doing business. We've been on the other end of getting an expansion team (Nashville joined the NHL in 1998-99). I'm happy for Vegas to some extent, but with all due respect they're probably getting better players than we did to start with. We will do the best we can to protect as many assets as we can."
The NHL Expansion Draft will be held June 17-21, with the announcement of the selections to be made at the 2017 NHL Awards and NHL Expansion Draft presented by T-Mobile on June 21 (7:30 p.m. ET; NBCSN, SN).
Teams must submit their list of protected players by 5 p.m. ET on June 17. Vegas will be given the lists at 10 a.m. on June 18 and will have until 10 a.m. on June 21 to submit its selections.
A team must protect seven forwards, three defensemen and one goaltender; or eight skaters (forwards/defensemen) and one goaltender.
Any player with a no-movement clause in his contract at the time of the expansion draft must be protected unless he waives it. All first- and second-year professional players, and unsigned draft choices, are exempt from selection by Vegas and do not have to be protected.
Poile also is waiting on center Mike Fisher to decide if he wants to play next season. The 37-year-old Predators captain can become an unrestricted free agent July 1.