Al Habsi, 26, can buy out the remainder of his contract for £300,000.
Brown reckons he would be a good acquisition even though he has spent most of his time at the Reebok as understudy to Jussi Jaaskelainen.
Hull keeper Boaz Myhill was solid last season and played a key role in helping the Tigers into the Premier League, but Brown is keen to recruit a keeper with top-level experience.