Leeds confirmed they had permission to discuss personal terms with Wise and Uruguayan Poyet, who both played in midfield for Chelsea before joining Millwall and Tottenham Hotspur respectively.
Former England player Wise took over at Swindon in May after their relegation to the Football League's bottom division.
He is well known to Leeds chairman Ken Bates, having played for Chelsea during Bates reign before managing Millwall from October 2003 to May 2005, leading them to the 2004 FA Cup final.
Leeds sacked Kevin Blackwell in September and said tonight that caretaker boss John Carver had left the club.
David Geddis was expected to take control for Tuesday's League Cup tie against Southend United.