The former Magpies striker says Benitez must keep the club up for the following reason.
The Magpies beat Swansea City 3-0 on Saturday to take maximum points for the first time since Benitez's March appointment.
The North East side are now two points from safety with a game in hand as they approach the season's final five fixtures and Quinn said earlier this month that he expects the Spaniard to walk away if he cannot prevent relegation.
As such, the Liverpudlian has once again stressed the importance of remaining in the division.
"I think they’ve got probably the best manager since Sir Bobby Robson was there, in regards of trying to build something," Quinn told the Alan Brazil Sports Breakfast show. "So it’s so important they do stay up because he could build a team for the future there at Newcastle."
Benitez previously constructed La Liga winning sides at Valencia and qualified Liverpool for the Champions League in five of his six seasons at Anfield.
The 56-year-old agreed a deal until 2019 on Tyneside, but admitted last month he does have a get-out clause inserted into his contract.
"Yes [there is a clause]," said Benitez. "Some people can see this as special, but it's normal. I am coming here trying to do my best to stay in the Premier League and if I have a compromise for the future, it's because I am convinced that we will do well. I want to stay here."
Robson qualified Newcastle for the Champions League in consecutive seasons during the early-2000s, having found the club inside the relegation places - albeit far earlier in the campaign.