The Austria international has found himself starting from the bench at the Weserstadion in 2011-12, and the Dutch club are said to be ready to pounce for his signature
The 22-year-old has started both of his side's Bundesliga fixtures on the bench this season, with coach Thomas Schaaf preferring Markus Rosenberg and Lennart Thy in attack.
Agents of the striker, Efe Firat Aktas and Giacomo Petralito, allegedly met with Werder officials on Tuesday and a transfer could soon be in the offing.
PSV, who know the Vienna-born man well as he played in the Eredivisie for Twente between 2006 and 2009, are thought to be waiting in the wings to launch an approach for the player. There may also be interest from a number of Ligue 1 outfits, but as of yet there have been no concrete offers.
Arnautovic has had a troubled career to date, and has only scored five goals for Bremen since joining the club in June 2010.