Mason, 25, is 19-12-5 with a 2.57 goals-against average and a .915 save percentage.
Bobrovsky, 25, the Vezina winner as the league's top goalie last season, took a 16-11-2 record, a 2.55 GAA, and a .915 save percentage into Thursday's matchup. He had won a franchise-record eight straight, during which he had compiled a 1.77 GAA.
"He's a great kid and I'm really happy for Bob," Reese said, "but my priority now is Steve Mason and Ray Emery."
The Flyers sent Bobrovsky to Columbus for second- and fourth-round selections (promising goalie Anthony Stolarz and left winger Taylor Leier) in the 2012 draft. They also acquired a fourth-rounder (which they dealt for Simon Gagne) in the 2013 draft.
The Flyers acquired Mason last year for Michael Leighton and a conditional 2015 draft pick.
Bobrovsky had an outstanding rookie year (28-13-8, 2.59, .915) with the Flyers in 2010-11, but coach Peter Laviolette grew impatient with him as he struggled in the playoffs that season. The Flyers added Ilya Bryzgalov after the season and Bobrovsky was not comfortable in a backup role in 2011-12. General manager Paul Holmgren traded him to the Jackets.
"He was young with us, and when you're young, you're going to be inconsistent," Flyers coach Craig Berube said. "The more you play and build confidence, the better [you get]."
Bobrovsky was sidelined by a groin injury when the Flyers faced Columbus twice last month.
Scott Hartnell was moved from the second to the third line. Vinny Lecavalier went from left wing on the third line to center on the second line.