German newspaper Bild has claimed that the Magpies hold an interest in the 25-year-old - who has netted 15 goals in 35 appearances this season.
Rafa Benitez has made landing a new striker a priority with the Tynesiders' current top scorer, Ayoze Perez, having netted just six times in the Premier League this season.
And Fullkrug could be an ideal solution and, with a reported asking price of just Â£8million, could be within Newcastle's price range.
Competition for the striker is expected to be fierce though, with Watford, Leicester, Cardiff and Aston Villa among those reported to be interested.
Benitez has made no secret of his desire to land a new striker with the Spaniard keen to see his side start converting chances into goals - but has warned that this will come at a cost.
"When you see our stats, it’s quite interesting," he admitted."You can say that six goals is not too much. But, at the same time, we’re one of the teams in the top in terms of shooting and top nine in terms of shots on target, so we’re attacking. "With five games to play we were safe because we have good balance.“You can win scoring more goals that would be ideal, and you can win conceding less goals. “If you have both, you can win trophies.“If you want to bring a striker with a guarantee of more than 10-15 goals per season, you have to pay money for him, for sure,”