"I don't have a crystal ball, so I can't really give you a definitive answer. There is enough progress, which kind of gives me hope, anyway, that we can make a deal at some point."
Holmgren added that the two sides will talk again on Tuesday.
Bryzgalov was in Philadelphia for two days last week and toured the city, got to know the Flyers goalies coach, Jerry Reese, and even looked at potential homes in South Jersey, all while Winters negotiated with Flyers brass.
Since the Flyers acquired Bryzgalov's rights on June 7, the goalie has made it clear he would like to sign with the team.
"Like I said, on Friday, we know where they're at and what they want to accomplish," Holmgren said. "I think they know where we're at. Obviously to make a deal, there is going to have to be some sort of a compromise. It might take some time and we are going to keep looking at it."
At this point in the negotiations, Holmgren said that there needs to be a compromise on both the years and the dollar amounts that are being kicked around.
Bryzgalov, who will turn 31 on Wednesday, won 36 games last season, with a 2.48 goals-against average for the Phoenix Coyotes and is expected to command somewhere between $5.5 million and $6 million in annual salary.
The salary cap number plays a large role in what happens with Bryzgalov and how many of the current Flyers could remain his teammates. Holmgren said he doesn't know what next year's cap number will be just yet, but TSN in Canada reported Monday that the teams and agents are being told the 2011-12 salary cap will be set at $64 million, with a $48 million floor. The Flyers currently have nearly $59 million tied up in 18 players for next season.