The former Leeds defender has been discussing the Uruguayan's time at Elland Road.
Wise was in charge of the Yorkshire side during a difficult time for the club in the lower divisions, with Poyet working alongside him as assistant.
And the former Sunderland boss was recently linked with the Leeds job by the Daily Mirror before they eventually appointed someone else.
The Uruguayan was said to have turned the club down but Heath has revealed what life was like at Leeds when Poyet was assistant - and how things could have potentially unfolded at Elland Road under his management.
Indeed, the Whites' former defender says Poyet would join in during training and, along with Wise, make players feel at home:
"Number one, you knew what they had done in the game. Number two, you had to up your game and couldn’t fool them. They joined in the odd five-a-sides and they still bossed it and you knew what they could do and wanted.
"They wanted a laid-back mentality where they were part of us. We were all a team. It was a real good blend."
Things may have changed a little since then, of course, with Poyet taking a number of posts in management.
Those at Brighton may have had a totally different lasting impression of the Uruguayan than those at Sunderland.
Leeds have gone in a different direction with Uwe Rosler but, considering owner Massimo Cellino's track record, Poyet could still end up at Elland Road this season...