Newcastle United are currently one point away from safety.
Benitez was appointed by Newcastle last Friday, to take over from Steve McClaren at St. James’ Park.
It is widely thought that the Spaniard will be a good managerial appointment for the Tynesiders, but he is in a race against time to save the club.
Newcastle are stuck in 19th place in the Premier League table, and they are one point away from safety.
Benitez now has just nine matches left to guide Newcastle out of the relegation zone, but Wright believes that the former Real Madrid boss may stick around even if his new side were to drop down the divisions.
"I think that if Newcastle do go down, with Rafa Benitez to get it going again, I think that he’ll probably stay and bring them back,” the former Arsenal striker said. “Then when Newcastle come back it could be under Rafa. It could be exactly what’s needed.”
Benitez took charge of his first Newcastle match yesterday, when he took his side to the King Power Stadium to face Leicester City.
The Magpies’ performance in the contest was an encouraging one, but they could not pick up any points.
Leicester striker Shinji Okazaki scored the only goal of the game, to leave Newcastle still looking for their first away victory of 2016.