The paper report that Allardyce has held talks with the Black Cats, and Poyet feels Allardyce could succeed at the club who sacked him last season.
He said: "He knows the Premier League inside out and he knows exactly what a team needs to do to stay in the Premier League.
“He has done it everywhere he has been so it’s not something new. That experience of being there for so long will definitely help."
Poyet also to Allardyce's ill-fated spell at Newcastle as being helpful to him in terms of settling in the region, but it is the manager's experience playing at Sunderland which will be of biggest benefit to him.
The Uruguayan added however it would only work if Allardyce is a long term appointment, rather than a quick fix until the end of the season.
Poyet was appointed as Sunderland boss in October 2013, and was fired this March, after a mixed 18 months at the club, which saw him lead them to the Capital One Cup Final, but fail to move them up the Premier League table.
The Sun report Sunderland have told the former West Ham and Blackburn boss to name his own terms, so desperate are they to seal his appointment.