The former Gunners midfielder, who formed part of their famous 'Invincibles' side, believes the Chilean is Arsene Wenger's best player.
The 37-year-old says he was so impressed with the former Barcelona star after the 2010 World Cup that he wanted Wenger to bring him to Arsenal that summer.
As it happened, the Gunners signed Sanchez for £35 million - but only after this summer's World Cup in Brazil.
Ljungberg is, however, delighted the deal has gone through and believes the Chilean can help Arsenal go 'all the way' this season.
When asked who the Gunners' best player is, Ljungberg told SportsKeeda: "I love Alexis Sanchez. I wanted the club to sign him after the 2010 World Cup in South Africa. I'm glad we did now, even though it was after four years."
And when pushed on Arsenal's title chances this year, the Swede said: "I think they'll go for it. They can do it. With a much stronger squad, they can go all the way.
"The club was under a financial strain over the past few seasons. But we're back with the big boys now. We've got some great players in the squad.
"I'm really excited and so are the fans. I believe the mentality is a big factor this season and there are a lot of players in the squad with positive belief."
Sanchez has enjoyed a promising pre-season with Wenger's side, taking part in the Emirates Cup and the Community Shield.
|Team||Pos||Dribbles Won / app||Goals / app||Assists/ app||Apps||Mins|
|Ángel Di María||Argentina||MF||5.00||0.20||0||5||422|
As Opta stats show, meanwhile, the Chilean averaged the second-highest tally of dribbles won per game at the World Cup.
Only former Barcelona team-mate Lionel Messi out-dribbled the direct 25-year-old, while Sanchez almost averaged as many goals per game, while also registering more assists per appearance than Messi.
Arsenal fans will no doubt hope Sanchez now hits top gear and provides the Gunners an extra dimension going forward. The only decision for Wenger is whether to start him out wide or replace Olivier Giroud down the middle.