Since these deals are non-binding at this point, I wonder if Chicago would try to get Asik to agree to the same amount of money and years (3 years, $25 million) while structuring it differently. Basically, tell Asik you're going to match, and try to get him not to sign an offer sheet with Houston at all.
EDIT: Of course, if I'm Chicago I'm not sure I match this. If I did, it would only be for purposes of trading him. You can't pay your backup center $8 million per season, and a Noah/Asik front court doesn't work even if you amnesty Boozer.