The former Leeds United player would have welcomed the Sunderland boss at Elland Road.
Both Moyes and Garry Monk were out of work when the latter was sworn in at Elland Road, with the Scot later hired by Sunderland.
After a slow start, Monk has Leeds within touching distance of the Championship play-offs, while Moyes' Sunderland are propping up the Premier League after failing to win any of their opening 10 fixtures.
Moyes was once one of the country's most highly-rated bosses, following an 11-year spell in charge of Everton. However, after disappointing spells at Manchester United and Basque side Real Sociedad, the 53-year-old's stock has fallen considerably in recent years.
Couzens, though, would have welcomed him at Leeds.
"Garry Monk was a great signing for us," the 41-year-old told the V2 Football Podcast's The 72 Show.
"I think everybody who knows football and who was in football has said that. But I would have liked David Moyes as well, because that was nearly there, I believe."
Moyes is the bookmakers' favourite to become the Premier League's next managerial casualty, with Sunderland already eight points adrift of safety ahead of Saturday's trip to Bournemouth.
But Monk, in contrast, is perhaps in the most secure position of any Leeds manager throughout Massimo Cellino's reign.