The Owls announced the double signing of Lewis Wing and Bailey Peacock-Farrell on loan from Middlesbrough and Burnley, respectively, on Tuesday.
Sheffield Wednesday have added six new players to their squad during the ongoing transfer window, but do not intend to put an end to their recruitment yet.
Darren Moore’s side are hopeful of bringing in more fresh faces before their EFL Cup match against Huddersfield Town on Sunday and one deal is said to be close.
The League One club are rated as very close to finalising a deal for 25-year-old midfielder Byers, who plies his trade for Championship outfit Swansea.
Barring any late hiccups, Sheffield Wednesday could acquire the services of the Scot from the Swans in the next 24 hours, with the signing seemingly in the pipeline.
Byers has been on Swansea’s books since the summer of 2016, but has found regular playing time hard to come by in the recent seasons.
The 25-year-old spent the latter half of last season on loan at Portsmouth and now looks to be on his way to join Moore’s Sheffield Wednesday.