Arsenal ended their 22-year wait for the title last week after Pep Guardiola's Manchester City slipped up at Bournemouth in the final week of the season.
Mikel Arteta's side now has the chance to join only Manchester United and Man City in winning the Premier League and Champions League in the same season, but Neville has warned how difficult it will be against Paris Saint-Germain, who are looking to win the competition in back-to-back years.
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"This is an incredible opportunity to stretch beyond anything you could ever imagine as an Arsenal fan, because they've never won that trophy. And that's the next step after winning a league," he said.
"I'm really happy for them for what they've achieved this week, they should celebrate it, and they have. But now they've got a Champions League final, if they can go win that next weekend, they'll have beaten the best. They'll have to beat a Luis Enrique Paris Saint-Germain team and a Pep Guardiola Manchester City team. That's the way to do it.
"If you're going to go and win your first Premier League title for 22 years, go and beat the greatest of all time. If you're going to go and win the Champions League, go and beat the current holders and one of the greatest managers that Europe has seen in the last 10, 15 years.
"It's going to be tough for them. PSG are a different level. They've got one of those managers who is just a serial winner, that horribleness inside them that they'll do anything to win.
"Luis Enrique is probably the greatest manager in the world right now, with Pep Guardiola. This is his moment. Arsenal are going to be right up against it. If you can win back-to-back Champions Leagues, you put yourself on a different planet. And that's what he wants, he wants to beat all the records.
"It's going to be very difficult for Arsenal because they're up against a team that are special and know how to do it.
But they know how to defend. They've got some matchwinners themselves. Both teams are fantastic physically. I'm really looking forward to it.
"I think PSG are the best team in Europe right now. Arsenal are going in as underdogs and have to scrap and fight and get over the line somehow if they're going to win it."
Neville believes Arsenal winning the title before their final game at Crystal Palace, in which they heavily rotated, is ideal preparation for the final on Saturday.
He said: "Do you know what was so good for Arsenal? Them winning the title four, five days early to allow them those extra days of preparation for this game.
"It's important for them that they've got that extra four or five days. It gives them a free week now and five or six days of really good quality build-up.
"They're not in recovery mode, the players that will start against PSG."
