Houston should keep Asik. Dwight Howard was at his most effective when he had a capable big backing him up, in Gortat. The Rockets probably don't want to deal with Asik's $14m deal for 2015, but he will be an expiring deal next season and some under the cap team would take him off their hands.
ESPN Kevin Pelton is guestimating the 2014 cap line at $58.5 million. Houston is at $34.5m now that they've dumped T Rob. Throw in cap holds of $4m for all the second rounders that will fill their roster, as well as guaranteeing Parsons and Greg Smith, and the Rockets have enough room to offer Howard a max deal for 4 years without moving Lin or Asik.
The Rockets are scrambling to move one or both of them because they don't want to pay the poison pill salary of $14m for either of them in 2015. If they can move both of them for expiring deals, they could sign Howard this summer and another max or near max FA next summer.
If Houston wanted to get away from Asik's deal bad enough, they could take Bass and Melo for him. Bass plays well with Howard, because he can spread the floor. Melo would be a project with only one more year of guaranteed money. It's a way better deal for Boston, who would be rewarded for taking on the $14m last year of Asik's deal.