The full-back is out of favour at Leeds under Marcelo Bielsa and has slipped down the pecking order.
While Leeds are not pushing to offload him, he faces the prospect of little in the way of playing time if he stays at the club beyond the domestic window deadline next Friday.
Both Watford and Blackburn have shown interest in him but, according to The Athletic, it is the Hornets who are keener.
Watford have made more of an effort to explore doing a deal to sign Douglas.
The Championship side have yet to become serious with their interest, but there is time for them to pull the trigger on a move.
Douglas clocked 15 appearances in the Championship for Leeds last season as Bielsa regularly preferred other options at left-back.
If the 31-year-old does stay at Leeds beyond next Friday, he will only have to wait 12 weeks for another chance to move, with the January transfer window scheduled to open.
