Brassard had been shopped for the better part of the season, and was almost moved to Ottawa last month.
Carter, meanwhile, is starting to hear the trade chatter surrounding him getting louder and louder, the Columbus Dispatch reports.
Carter, who has struggled this season while battling injuries, is being actively shopped by Blue Jackets GM Scott Howson, who acquired him from Philadelphia last summer.
"There's not much I can do about that," Carter told the Dispatch. "That's something I can't worry about or control. My main focus right now is just getting healthy and getting back into the lineup.
"There's talk about a lot of guys (in here) right now. Our team, with the way the season has gone -- the injuries, the standings, and stuff -- I don't think it should come as a surprise to anybody on our team if they end up (in rumors)."
It has been widely reported that Carter has been disappointed in Columbus and would welcome a trade, though he insists he's never requested to be moved.
"I haven't asked for a trade," Carter said. "Nothing. I'm here to play hockey."
Howson, who recently met with Carter's agent Rick Curran, has several players he's expected to move before the Feb. 27 trade deadline, including forwards Vinny Prospal, Kristian Huselius and Antoine Vermette.
More Trade Deadline Info
List of Trades
| No-Trade/No-Movement Clauses
| Top 25 Available Players
| Team-by-Team Cap Info