Despite those rumours, Marshall is only focusing on keeping the 18th-placed Bluebirds in the top flight following their promotion last season.
"I am desperate right now to try to help keep this club in the Premier League," he told Wales Online.
"At this moment in time my personal career does not really come into it. I am going to be judged over these last games now. That's me, all the other players and the club as a whole."
Cardiff continue their fight for survival on Saturday when they entertain fellow strugglers Crystal Palace.