Sundin could do what Teemu Selanne and Scott Niedermayer did last summer and wait until mid-season to join a team.
"It's possible," Barry said. "It's not something that's preferable even to him. Mats has said in the past it's not something he is totally comfortable with, but at the same time you can't say that until you're in that position yourself. Niedermayer went through this and needed time and perhaps Mats is in the same situation."
The Vancouver Canucks, Toronto Maple Leafs, Montreal Canadiens, New York Rangers, Philadelphia Flyers and New York Islanders are all interested in Sundin.
However, the longer the 37-year-old waits, the greater the chance that some teams drop out of the race.
"I understand a bunch of these teams are going to start making moves if they don't hear from him," Barry said. "Probably by about the end of the month, they are going to start making some Plan Bs and he knows that. He has known that since July 1, really. Any of these teams could have changed their minds at any point in time, there's nothing in holding them back to do that."
