Houston also is expected to sign Bulls center Omer Asik to an offer sheet. Earlier in free agency, Asik agreed to a three-year, $25 million offer.
The Rockets turned back to Lin after the unrestricted free agent Dragic signed a four-year, $30 million deal with Phoenix.
The 7-foot Asik was playing professionally in Turkey when he was picked by Portland in the second round of the 2008 draft and immediately traded to Chicago in a three-team deal. He played in 66 games last season, but only averaged 3.1 points, 5.3 rebounds and one block per game. Asik helped Turkey earn the silver medal at the 2010 FIBA world championship.