Leeds have made known their interest, but his old club Millwall appear to be leading the chase.
Other clubs believed to be in the hunt for the 31-year-old are Sheffield Wednesday, Burnley, Cardiff, Walsall, Plymouth and Championship newboys Doncaster and Swansea.
The Lions have already spoken with Byfield about a return to the New Den, just under 10 months after leaving for the West Country in a £100,000 move.
But Leeds are being tipped to hijack their bid, with Gary McAllister keen to bolster his strike force ahead of another League One campaign.