The Sunday Mirror says Campbell,34, dramatically walked out on Notts County on Tuesday just one game into a five-year £40,000-a-week deal with the League Two Magpies.
But now Brown will revive his interest in Campbell, who he sees as the star to solve City's defensive problems following the £6million sale of Michael Turner to Sunderland last month. Campbell will not be able to sign for the Tigers until the January transfer window opens, when he will be available on a free.
A Hull source revealed: "Sol has been a target before and his experience and organisational skills are what the team needs."
But Brown is bracing himself for a fight with top-flight rivals Aston Villa, Tottenham and West Ham for Campbell.