Nottingham Forest have already made a bid for the Jamaican, which was rejected in the summer transfer window.
And now Burnley, with their manager Brian Laws understood to be a keen admirer, and Leeds are also tracking the player.
There is a chance the player could be signed in an emergency loan deal, with a view to making the move permanent in the January transfer window.
Johnson is in the final year of his contract, and Wednesday could lose out on much-needed money if he stays until next summer.