Bild claim the two Premier League clubs will be at the front of the queue for the 29-year-old's signature in the summer.
Wagner, who was linked to six clubs in 2016, has scored 10 Bundesliga goals in 17 appearances for Hoffenheim so far this term.
Reports in April claimed Swansea, WBA, Southampton, Sunderland, Middlesbrough and Aston Villa were chasing his signature, but he left Darmstadt in a £2.5million move last summer.
Under contract to 2019, Wagner's price-tag is likely to have doubled after his productive season for the Champions League-chasing club.
A physical presence in the box, he could be an ideal fit for Swansea if they lose Fernando Llorente to Chelsea.
Swansea last week