The Sunday Mirror says Brown believes he can land the former Spurs ace at the second time asking.
Brown failed to land the 34-year-old in the summer because he refused to hand him more than a 12-month contract.
A Hull source revealed to the Sunday Mirror: “Sol has been a target before and his experience and organisational skills are what the team needs.”
Campbell left Notts County earlier this week just a month after signing a five-year contract with the club.