The moves were announced on Tuesday, one day after the players were placed on waivers following New York's rough 1-4 start to the season. The Rangers recalled centre J.T. Miller and goalie Cam Talbot from Hartford to replace them on the roster.
Biron, the 36-year-old backup to Henrik Lundqvist, is 0-1 with a 7.61 goals-against average and .763 save percentage in two games. Over four seasons with the Rangers, Biron is 22-15-3 with a 2.47 GAA, and .908 save percentage in 46 games.
He relieved Lundqvist in the second period at San Jose on Oct. 8 and allowed five goals on 21 shots in New York's 9-2 loss. He then started four days later at St. Louis and was pulled after two periods after yielding four goals on 17 shots in a 5-3 defeat.
This could mark the end of Biron's NHL career.
The 35-year-old Asham has played in three Rangers games this season. Asham struggled just to make the opening night roster, and he too could be coming to the end of his NHL career. He registered his 1,000th NHL penalty minute at Anaheim on Thursday.
He has no points, 14 penalty minutes and a minus-3 rating this season.
Miller, 20, is tied for second in the AHL with four goals in three games after being sent down following New York's opening-night loss at Phoenix. Miller had one shot in nearly 12 minutes of ice time in that game. In 27 games over two seasons with the Rangers, Miller has two goals and two assists.
Talbot, 26, has earned wins at Hartford in two straight outings — stopping 64 of 70 shots. He is 2-0-1 with a 2.54 GAA and .918 save percentage in three games with Hartford this season.
He was originally signed by the Rangers as an undrafted free agent on March 30, 2010.