Holmgren was tied up in the general managers' meetings in Boston on Wednesday and said he planned to talk with Winter on Thursday.
Asked if Bryzgalov would accept a deal for less than four years, Winter said he would not negotiate through the media.
Holmgren implied that the length of the contract would not be a stumbling block.
"We want to get some kind of deal done," he said. "I'm not sure we have any preference, really, [on the length]. We have to see what the other side wants to do and try to come to agreement. I'm open-minded. Obviously, at the end of the day we want to sign him."
Bryzgalov, an outgoing, colorful sort who is a student of Philadelphia history - he enjoys reading about Ben Franklin - said he would "very much like to have the opportunity to play for the Flyers."
The Russian goalie, who turns 31 later this month, thinks the Flyers are close to winning their first championship since 1975, saying they are "right there."
"I would love very much to be a part of the team that brings the Stanley Cup back to Philadelphia," he said. "It would be a great honor. And it's time!"
But in order to land Bryzgalov, the Flyers will have to make several moves to fit him under the salary cap.
They might decide to part with a solid defenseman like Matt Carle (a $3.4 million cap hit), or perhaps deal a goal-scoring machine named Jeff Carter ($5.3 million). The latter move seems more unlikely, because Carter has averaged a little over 38 goals over the last three years, and he became more well-rounded this season.
Carter was the Flyers' leader among regular faceoff men (54.7 percent) and he finished at plus-27.
If Carter stays, the team probably will not sign winger Ville Leino if it is able to sign Bryzgalov.
