Amundson, 32, averaged 4.9 points and 5.1 rebounds in 41 games for the Knicks last season.
Coach Derek Fisher praised Amundson’s demeanor and professional approach during New York’s disastrous 17-win season in 2014-15.
Amundson, 6-foot-9, will likely serve as a reserve forward for New York in the coming season.
Galloway, barring something unforeseen, is expected to be on the Knicks’ 15-man roster on opening night.
So that leaves three open roster spots. Ledo and Travis Wear may make the opening-night roster, depending on how each does during the Knicks’ summer league and training camp.
Thanasis Antetokounmpo may also earn a roster spot, depending on what he shows in summer league and training camp. (For more on Antetokounmpo's situation, click here.)
The Knicks have used all of their cap space. They still have the $2.8 million room exception and veteran’s minimum contracts to offer free agents.
New York has been in touch with representatives for free agent guard Alexey Shved throughout free agency, sources say. Shved played well for New York last season after being acquired in a trade in February.
In 26 games, Shved averaged 14.8 points per game, 3.6 assists and 4.6 rebounds.
The Knicks, according to league sources, offered Shved a veteran’s minimum deal earlier in free agency. Shved turned that offer down, as well as minimum offers from at least two other teams. Shved can also garner lucrative offers from teams in Europe, but his preference is to play in the NBA, sources say.
It will be interesting to see if the Knicks offer Shved their $2.8 million exception.
New York appears to have a need at wing and shooting guard, and Shved can help in that regard. New York also expressed interest earlier in free agency in John Jenkins, sources say. Knicks GM Steve Mills has remained in contact with Jenkins' representatives, but the shooting guard is not believed to be a strong candidate for one of the Knicks’ final roster spots at this point.