The firm is awaiting a decision later this month on whether it can transform the 25,000 sq ft building at Rockingham Business Park in Barnsley, which would create up to 70 new jobs.
The arena would house over 120 interconnected trampoline beds dedicated to open jumping, as well as dodgeball courts, bounce basketball, trick tracks and giant foam pits, alongside fitness classes, lessons, plus party and event rooms and a café.
The Go Air Group opened its first site, Go Air Cardiff, in November 2015. It also has a site in Mancheser and is soon to open in Swansea.
Marketing director Lisa Entwistle-Evans said: “The response on social media for the proposed Barnsley venue has been fantastic.”