The 27-year-old claims that if Allardyce can keep the Black Cats in the Premier League this season, he is capable of laying foundations of a new era in the club's history.
Cattermole said: "We've brought in the new manager and he has built things at West Ham. If we can stay up with what, in theory is not really his squad - and the club invest - then there is no better person to help us.
"So that's something we are aiming to do. We need to improve, we need to get better and climb the table."
The Black Cats are currently struggling in the 19th spot in the league table, four points from safety.