The 33-year-old Germany international returned to Bremen on loan in the summer after difficult spells with West Ham United and AC Milan. His comeback has proved an immediate success, with Füllkrug scoring 12 goals in 11 appearances across all competitions.
His performances have strengthened Werder's desire to keep him beyond the current season, and head coach Daniel Thioune has confirmed that the club and player share the same ambition.
Speaking to Transfermarkt, Thioune made clear that there is a willingness on all sides to continue the relationship.
"I think the desire is there from everyone. We as a club, I as the coach and Niclas himself are very interested in continuing to work together beyond the summer," he said.
Füllkrug previously enjoyed a successful spell at Werder between 2019 and 2023 before joining Borussia Dortmund and subsequently moving to England.
His time at West Ham failed to develop as hoped, while his loan spell at AC Milan also provided limited opportunities. Returning to a familiar environment in Bremen has allowed the experienced striker to rediscover his confidence and scoring touch.
He has also earned a return to the Germany national team under Jürgen Klopp, who selected him for the November Nations League fixtures after his impressive start to the campaign. Füllkrug scored nine Bundesliga goals in his first nine league appearances, placing him at the top of the division's scoring charts when the squad was announced.
However, a permanent agreement will not be straightforward. Füllkrug remains contracted to West Ham until the summer of 2028, meaning Werder must negotiate with the English club if they want to retain him beyond his loan.
The financial terms of any deal will therefore be important, with West Ham holding the contractual rights to the forward.
Thioune's comments nevertheless indicate that Bremen would welcome the opportunity to make the move permanent. Füllkrug's return has provided the club with an experienced goalscorer, while the player himself appears to have found a situation in which he can again perform at his best.
The coming months will determine whether the three parties can reach an agreement, but Werder have made their intentions clear.