That is not totally correct. I see 21M available here.
If all free agents are announced, Boozer is amnestied, Taj dumped, Dunleavy dumped and Murphy waived
Derrick Rose $18,862,876
Joakim Noah $12,200,000
Jimmy Butler $2,008,748
2014 1st (Bobcats) $1,898,300
Tony Snell $1,472,400
2014 1st (mid-first) $1,395,400
Nikola Mirotic (hold) $1,075,300
cap hold $507,336
cap hold $507,336
cap hold $507,336
cap hold $507,336
Rip Hamilton (stretch) $333,334
Available: $21,224,298
That is a significant amount of cap space.
Carmelo would have to take an additional pay cut in his first-year salary to sign. If he signs for exactly $21,224,298, then it would be a 4 year, $90.8 million contract. That's 6 million less than his full non-bird max.