Big Time Rush is going on their own tour soon ... but, they're not above going back to being an opening act -- for one big-time band that is.

We caught up with the popular boy band in Los Angeles Friday night ... and, we asked them what reunion tour they'd most want to see -- and all four of the guys say it has to be *NSYNC.

Kendall Schmidt, James Maslow, Logan Henderson, and Carlos PenaVega all say they'd love to see the early 2000s group get back onstage together ... but, they think Justin Timberlake ultimately has to want to do it.

The group even tries to entice *NSYNC to reform by offering up their own services ... promising to open for the band if it would get them back onstage.

As you know ... talks of an *NSYNC reunion have swirled since the group got together to record "Better Place" -- their hit single from "Trolls Band Together."

There hasn't been any concrete movement since ... but, the sense is that most of the band would be down to link back up -- as long as JT is in the mix.

BTW ... Big Time Rush has their own tour starting soon. The four main members will appear alongside Katelyn Tarver and Stephen Kramer Glickman, who both played major roles on the hit Nickelodeon show that launched BTR into fame -- and, they held a pop-up event in L.A. to get fans excited.

We also asked the band about what the vibe of their tour is like ... and, ya gotta listen to their answer for yourself.

Unclear if their offer will be enough to sway the *NSYNC team ... but, it would be a 'Big Time' opening act!