The Spaniard hasn't been himself this season, but Neville says a new deal until 2023 could settle the 28-year-old.
Neville told Sky Sports: "De Gea has had a difficult time in the Premier League and he's had difficulties at home where he's lost his place in the national team. I don't think he's fully recovered from the poor World Cup in 2018, and he's made more mistakes in the last 15 months than ever before.
"But I've got to believe that this is good news and hope that what's happened in the last 12 to 15 months has been a result of the ongoing speculation. The hope is that now he's signed, he can settle down and start performing.
"United need a spine. They had eight academy players in the squad on Saturday, but their problem isn't the academy. The problem is that they haven't got a strong, dominant spine, but De Gea can be the start of that."