The deal includes an option to buy, and Fullkrug is reportedly happy to take a significant salary cut to make the move permanent, as per Sky Sports.
The 33-year-old is under contract with the Hammers until the summer of 2028, and has now re-joined the club that he started his career with.
The German forward scored just three times for the East London oufit after joining from Borussia Dortmund in 2024, and spent the second half of last season on loan at Milan where he netted once in 20 Serie A appearances.
Fullkrug will hope he can gain his confidence back in his homeland at a club where he scored 45 times in 90 appearances.
He will now work under manager Daniel Thioune, and could be poised to feature in Bremen's away trip to LSK Hansa in the DFB Pokal first round on Saturday.