The 21-year-old Belgian forward netted seven Ligue 1 goals last term, and already has three to his name in 2015/16.
Reports from the Daily Star, citing L’Equipe, reveal that there was strong interest in Batshuayi from sides in England during the window just gone, but that no suitors could match l’OM’s asking price, with a £22m offer understood to have been rejected.
However, it’s now claimed that both Arsenal and Spurs could makes moves for the youngster in January, with the clubs keen to bolster their striking ranks.
Arsenal were linked with a host of centre-forwards over the summer, but ultimately failed to bring in a new name leaving Arsene Wenger with Olivier Giroud and Theo Walcott as his options.
Meanwhile, Spurs chief Mauricio Pochettino has only Harry Kane as an orthodox spearhead with Emmanuel Adebayor having been released over the weekend.