The 24-year-old's agent Richard Motzkin has confirmed that he has travelled to Malmo, who are one of Fulham manager Roy Hodgson's former clubs.
Motzkin told Eurosport.se: "I have been in Malmo, but I have no further comments."
Malmo are looking to replace Ola Toivonen, who has joined PSV Eindhoven, although the club would not be drawn on any interest in Johnson.
Sporting director Hasse Borg said: "I might have heard of the player and his name."
I'm not sure how it works with transfer widows and stuff but if we manage to offload him and free up those wages then it'll be a great move.