"We got our foot in the door now," Holmgren said in a conference call with reporters on Tuesday night. "We have some time to look at certain things and try to work through the issues and get a deal.
"We didn't make this trade to acquire his rights just to try to hang around."
Signing Bryzgalov might force the Flyers to deal a high-priced player such as Matt Carle or Jeff Carter, and perhaps make it impossible to re-sign Ville Leino, a prospective free agent.
"We still have intentions of trying to re-sign Ville . . . but you can only do so much," Holmgren said. "We're trying to have the best team available. We'll see what we can do."
Flyers goalies struggled during the playoffs, compiling a 3.46 goals-against average - 14th out of the 16 playoff teams.
Bryzgalov went 36-20-10 with a 2.48 goals-against average and .921 save percentage in 2010-11. He recorded seven shutouts, which is seven more than the Flyers posted.
He struggled in this year's playoffs, going 0-4 with a 4.36 goals-against average and .879 save percentage.
Bryzgalov, who turns 31 on June 22, reportedly is seeking a four- or five-year deal; he is expected to command at least $5 million per season.
"We'll see what we can do. He's certainly not an old goalie, and we feel he has a lot of good years ahead of him," said Holmgren, adding he has yet to have contract talks with the goalie's agent, Rich Winter.
After the season, Ed Snider, the chairman of the Flyers' parent company, Comcast-Spectacor, said he "never again" wanted to go through another goalie carousel like he did in this year's playoffs.
The Flyers already have nearly $59 million committed to 18 players for 2011-12. The salary cap is expected to climb from $59.4 million to about $62.4 million for next season, and it won't be announced until after Boston and Vancouver finish the Stanley Cup Finals.
As it stands, the Flyers cannot sign Bryzgalov under the current cap - unless they deal salary.
The Vezina Trophy runner-up two seasons ago, Bryzgalov was the backup goalie when Anaheim won the 2007 Stanley Cup. Current Flyers defensemen Chris Pronger and Sean O'Donnell were on that team.
If he is signed, Bryzgalov will be a positive influence on fellow Russian goalie Sergei Bobrovsky, Holmgren said.
A native of Togliatti, Russia, Bryzgalov has been in three Olympics (2002, 2006, 2010), winning a bronze medal at Salt Lake City in 2002.
Four years ago, the Flyers had success in dealing for pending free agents, signing Scott Hartnell and Kimmo Timonen. However, they were unable to sign Evgeni Nabokov and Dan Hamhuis after acquiring their rights last year, though they did move Hamhuis' rights to Pittsburgh for a third-round pick in this year's draft.
Clackson, 26, was selected by the Flyers in the seventh round of the 2005 draft. In his AHL career with the Phantoms, he had six goals, 13 assists, and 574 penalty minutes in 204 games.
Contact staff writer Sam Carchidi at firstname.lastname@example.org or follow on Twitter @BroadStBull