Liverpool were thought to interested in the former Hamburg man and may again look to make a move if Elia's prposed switch to the Weserstadion falls through.
The winger passed a medical at the Bundesliga side on Sunday and was expected to sign a four-year deal on Monday. However, the move has now been delayed following the dispute between Elia and Juve.
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"The contract between Juventus and Elia has yet to be terminated. That's why he has not signed with us yet," Bremen director Klaus Allofs commented to Bild.
"It's about a few material things. There's nothing we can do about it to solve this. I don't know whether this is insurmountable."
The 25-year-old arrived at Werder Bremen's training camp in Norderney earlier on Monday, but won't be allowed to train until his Juve deal has been settled.