Despite having signed a new contract in the summer, Johnson's face clearly does not fit with manager Xisco Munoz, and it would suit all parties if he could leave before Friday's 11pm deadline.
But as of yesterday, Munoz told the media there had been no concrete interest in the winger, a key figure under Darren Moore.
Paul Warne's Rams are believed to have entered the fray, but are thought to be haggling over a loan fee for the player, according to The Telegraph.
At the same time, the Owls are working to tie up signings with loans for Jeff Hendrick and Alex Mowatt believed to be in the pipeline. They had also hoped to sign Hendrick's Newcastle United team-mate Isaac Hayden, but the former Hull City midfielder now looks more likely to go to Standard Liege.
Their chances of signing Blackburn Rovers midfielder John Buckley do not seem dead after all after Swansea City reportedly failed in a £3m bid because the player who scored twice in the midweek 8-0 League Cup win over Harrogate Town did not want to move to south Wales.
Deals must be completed by 11pm on Friday.