Rules:
1) You must keep the team under the luxury tax, and not cheat by sending huge amounts of cash to a team to keep us under the tax that effectively have us paying the same as if we paid it.
2) We'll use an estimated luxury tax o 68.5 million since that's what Chad Ford's expert predicted, and I have no better guess
3) NBA minimum roster is 13, so you have to add four players total to the presently guaranteed contracts
4) NBA minimum salary for a player with 0 experience next year is $457,588
5) I will assume our draft picks are 16 and 25 for the sake of argument. Pick #16 costs $1,593,600 assuming we pay the 120% rookie scale contract which everyone gets. Pick #25 costs $1,039,800

Present salaries:
Joakim Noah $2,445,680
Tyrus Thomas $4,743,598
Derrick Rose $5,184,480
John Salmons $6,274,400
Tim Thomas $6,466,600
Jerome James $6,600,000
Kirk Hinrich $9,500,000
Luol Deng $10,365,000
Brad Miller $12,250,000
Total: $63,829,758
Total with rookie contracts and one min level contract (leaving one roster spot): $66,920,746

A sample base salary: 6/50, year 1 salary 6.6 million
Contract Calculator can be used to figure out year 1 salary for Gordon based on total contract size, just enter the total salary and years and hit submit.

If you assume that 6.6 million base salary (which could be low if he gets a better offer from Oklahoma) and that we keep our rookie deals then we need to free up aproximiately 5.03 million in salary to squeeze him in under the tax.