Forwards Matt Moulson, Drew Stafford and Cody McCormick, and defensemen Christian Ehrhoff, Henrik Tallinder and Tyler Myers could all be moved in the coming days.
Goalie Jaroslav Halak and right wing Chris Stewart, acquired from the Blues, could also be dealt, as teams have also inquired about them.
Moulson is the most coveted of the Sabres' players, with a number of teams competing for his services.
The Los Angeles Kings, Anaheim Ducks, Phoenix Coyotes, Ottawa Senators, New Jersey Devils and Vancouver Canucks have all inquired about Moulson.
The Senators are also interested in Stewart, who has one-year left on his contract beyond this season.
In exchange for Moulson, the Kings are looking for a first-round draft pick and a top prospect or NHL-ready talent as part of a package.
Ehrhoff, meanwhile, is also a very attractive piece for several teams looking to bolster their blueline. He has six-years left on his contract and comes with an annual salary cap hit of $4 million.