The Spain international moved to Old Trafford from Atletico Madrid in 2011. After a difficult start to life in England, the 27-year-old has established himself to become one of the best goalkeepers in the world.
De Gea almost single-handedly made sure Sevilla were not successful in finding the back of the net in the first leg of the Champions League Round of 16 tie at the Estadio Ramon Sanchez Pizjuan on 21 February. He also has 15 clean sheets in the Premier League this season, which is the highest in the league.
Parlour played in an Arsenal side that had two excellent goalkeepers in David Seaman and Jens Lehmann, and won the league with the Gunners.
As for Liverpool, he believes the mistakes made by Simon Mignolet and Loris Karius have cost Liverpool points this season.
"If Liverpool can find a target like David de Gea, they have every chance of winning the league," Parlour told Sky Sports.
"You always have to have a good goalkeeper, at times they keep you in games. When I was at Arsenal, Seaman and Lehmann kept us in games, they didn't make mistakes at the wrong time. Liverpool goalkeepers have made big mistakes at the wrong time and that's cost them."
Former Tottenham Hotspur manager Tim Sherwood agreed with Parlour's comments. He has backed Jurgen Klopp's side to make an approach for AS Roma's Alisson Becker to strengthen the Reds' goalkeeping position.
"Liverpool are the closest team to be challenging Manchester City," Sherwood explained.
"Yes, they lost Philippe Coutinho, which was a big blow, but they've coped without him. They look like they will need to find a replacement for Emre Can, he's a big player too, but they do have Naby Keita coming in the summer.
"Roma goalkeeper Alisson Becker is a good prospect. There's a lot of noise coming out of Liverpool. Perhaps he has a buy-out clause, otherwise they wouldn't be tracking him down as they reportedly are.
"The key for Liverpool's current goalkeepers are the mistakes they have made. Liverpool cannot gamble, they need a sure thing. It's a key position and you're not going to win anything without a top goalkeeper."