The 27-year-old has made 18 starts for the Bundesliga outfit this season, but a developing trend of having him come off the pitch early and using him as a substitute made him frustrated.
He has been, recently, subbed off at the 76th minute during their fixture on Saturday against Borussia Monchengladbach, wherein the match ended in a 1-1 draw.
The Belgian international joined Bremen last summer and signed a contract that ties him to the club until 2016.
However, his recent revelations regarding his unhappiness with the way the manager has been treating him could see him take an early exit at the end of the season.
"I am always unhappy when I am not playing matches from the start. Therefore I am well able to imagine leaving Werder Bremen, although at this point in time I am unable to make a comment on the issue," Elia told Sky Sports.
"We will only be able to see what's on at the end of the campaign. Either I am to stay on or Werder Bremen is selling me then."