The two groups have not all met but share a connection through boyband McFly. Escala violinist Izzy Johnston dates drummer Harry Judd, while Saturdays singer Frankie Sandford is in a relationship with Dougie Poynter.
"It would be great if Escala and The Saturdays could meet up someday. We would love to collaborate with them," Johnston told the Daily Record.
"Since I met Frankie, The Saturdays have grown quickly as a band. I'm a big fan and we were gutted when they didn't get No.1 with their Comic Relief single."
"We love The Saturdays. Their last single 'Issues' was fantastic and their video for 'Just Can't Get Enough' was great," Tasya Hodges added.
"Their styling is really good, too. They wear great dresses and always look so fresh. They also have great voices."
Escala release their self-titled debut album on May 25, which includes covers of Snow Patrol's 'Run' and Robert Miles's 'Children'.