The immediately worrying thing for West Ham fans would be Poulsen's goal record. After all, the 24-year-old is hardly prolific, scoring just four times in the Bundesliga last season and five the year before.
But he is not that kind of forward, offering so much more than goal threat with his physicality and energy.
In that respect, he is the opposite of what West Ham signed last season in Javier Hernandez. The Mexican is a pure poacher, offering little to help the team with anything but goals.
But perhaps Poulsen can be the kind of player who gets the most out of players like Hernandez and even Arnautovic.
The reported West Ham target is a selfless player, willing to create opportunities and play the physical game that allows others the opportunity to take advantage.
Able to play both up top and out wide, Poulsen is a player who is part of the team, rather than a star to build around, and perhaps that is exactly what West Ham need right now.
He may not be the headline act, but Poulsen would give other players the opportunity to be.