Burnley are said to be circling the New Zealand international, and the Whites will move for the Bundesliga hitman if he moves on, according to Bild.
Recent reports suggest that Leeds have rejected a £16m bid for Wood from an unnamed club.
This coincides with rumours that Burnley want the prolific hitman to replace Andre Gray, who joined Watford for £18.5m this summer.
Lasogga, who has represented Germany at Under-21 level, has scored 26 times in 96 league matches for Hamburg.
The German club are said to be keen to offload him, to remove his £3m-a-year wages from their books.