The Uruguayan is the latest name on the Leeds owner's reported shortlist.
Poyet was sacked by Sunderland earlier this season and will be looking for a new post during the summer. The Uruguayan will reportedly want 'assurances' from owner Massimo Cellino, however, as he sees Leeds as a potentially risky move.
Poyet has worked at Leeds in the past, acting as assistant manager to Dennis Wise during a troubled time at United.
As for Redfearn's future, meanwhile, the Mirror speculate - as many others have done - that the 49-year-old looks increasingly likely to leave the manager's post at the Yorkshire club, with his contract expiring over the summer.
Even were Redfearn to stay with Leeds, it would likely be in a return to the academy post he previously held at Thorp Arch. Cellino was typically unclear about the coach's future during an hour-long press conference on Thursday afternoon.