Let's assume the Jazz renounce the cap holds for all their expiring players except Gordo, release all their unguaranteed players, and set the first year of Favors' extension at his cap hold. These are the salaries on the books for next year:
Favors: $12 016 392
Gordo: $8 630 458 (cap hold)
Kanter: $5 694 674
Burke: $2 548 560
Burks: $3 034 356
Evans: $1 794 872
Gobert: $1 127 400
Total: $34 846 712
Next, the Jazz have 2 first round picks (we can assume they don't sign second round picks for the time being). Let's assume both the Jazz and W's do relatively well, and the Jazz end up with the 8th and 22nd picks. We'll also assume that both sign for 120% of the rookie scale (pretty standard). The first year salary of those picks (again, at 120% of scale) is:
#8: $2 745 840
#22: $1 344 120
Total (including the 7 players above): $38 936 672
You can add roughly another $1mm for roster charges to bring the roster to 11 players (renouncing the last roster charge to sign a free agent).
Total: ~$40mm
So...with Gordo not signing an extension, no second round picks signing, and the Jazz and W's outperforming predictions, the Jazz will have about $20mm in cap space (depending on where the cap is set next season).
That's really only enough for 1 impact player.
If the Jazz just let Gordo walk, they'll be in the $30mm cap space range (depending on the cap, Favors' first year cap hit, where the Jazz pick in the draft), which could net the Jazz two good players.
edit: miscalculation.