According to a report from Bild, the Premier League duo are both keen to bolster their respective front lines and have identified the powerful forward as a plausible option ahead of the summer transfer window.
Wagner has been in decent form this season, netting a respectable total of 11 goals for Hoffenheim in the Bundesliga.
However, at the age of 29, there’s a chance that Julian Nagelsmann and his men behind the scenes could look to offload Wagner if a sufficient offer comes in from either of the top flight teams.
Standing at just over six foot four, Wagner would provide a physical presence to any team he joins and would certainly be a good suit to the Premier League if the Swans or the Hammers do choose to make a move.
Wagner has helped Hoffenheim to an impressive campaign, with them sat in fourth place on the Bundesliga table.