Singers Lene Nystrom ('memba her?) and Rene Dif and keyboardist Soren Rasted tell TMZ ... the band's set its sights on playing at Coachella next April ... which would be about 2 months before the Dutch-Norwegian band kicks off its '90s nostalgia tour.

How the band's gonna get it done is TBD ... but it's making a strong case for itself well ahead of Coachella announcing its highly-anticipated lineup. And, if it helps, the band -- famously known for its 1997 worldwide hit, "Barbie Girl" -- will be in the neighborhood.

Aqua recently announced it's making pit stops in 5 cities in Canada next June. Aqua's headlining and they'll be joined by fellow Dutch Eurodance group Vengaboys and Ace of Base's Jenny Berggren.

Aqua's undoubtedly excited to get back onstage next year but they make it crystal clear -- they've set their sights on Coachella. Check out the vid ... Lene tells us they'd fit in PERFECTLY 'cause, y'know, all the sex, drugs and rock & roll.

The group's ambitious goal is NOT far-fetched. Remember, a precedent's been set after 'NSYNC (sans Justin Timberlake) performed with Ariana Grande this year during weekend one.

Aqua -- which hasn't performed in the U.S. since the late '90s and teases about possible new music in the horizon -- is no stranger to syncing up with Lance Bass & co. -- they not only toured together, Lene says 'NSYNC's one of the bands they traveled with the most in the 90s.

So ... your move, Coachella.