Howard confirmed via Twitter on Friday night that he will sign with the Rockets.
Asik has no interest in being Howard's backup or playing next to him, a source close to the Rockets' center told ESPN.com. It is not yet clear if Asik would demand a trade.
It is possible the Rockets will look to engage the Atlanta Hawks in a sign-and-trade deal for free agent Josh Smith. The Hawks are open to making a sign-and-trade deal with the Rockets for Smith, league sources said. Smith and Howard played together on summer teams as teenagers and have talked in the past about becoming teammates in the NBA.
Asik, a quality defender who averaged career highs in points (10.1), rebounds (11.7) and blocks (2.7) while starting all 82 games for Houston last season, has a complicated contract that could become a challenge in a trade.
His official salary-cap number for this season and next is $8.3 million, but because of an arcane measure the Rockets used to sign him away from the Chicago Bulls last year, he is actually owed more than $20 million over the next two seasons. His salary in 2014-15 is guaranteed at $15 million.