The 'Everybody In Love' hitmakers are close friends with the girl band - with their respective singers Marvin Humes and Rochelle Wiseman in a relationship - and would leave to team up to record a special festive track.
Singer Jonathan 'JB' Gill said: "Will we see a JLS/ Saturdays duet? Wow. I don't know but we'd do it in a shot.
"We'd love to do a song with the girls. A Christmas number one maybe? Watch this space."
Oritse Williams said: "Who would do a Robbie? None of us. We're all here to stay but who knows what the future holds.
"There are cycles for everything and Take That are a great Example to follow. They disbanded, everyone went their own way and did different things, then they all came back together. What's to say that won't happen for us?"