Former Swansea defender Ricketts had been linked with a move away from the KC Stadium, with Portsmouth and Everton rumoured to be interested in the 27-year-old.
Bolton and Celtic were also thought to be tracking the £3m rated Welsh international who was a regular in the Hull side that dramatically survived top-flight relegation last season.
Swansea would have pocketed a percentage of any Ricketts transfer as the deal that took him away from Swansea included an undisclosed sell-on clause.
But Brown has insisted he wants the full back to remain with the Tigers as Hull plot a fresh Premier League assault.
"He has got another year left on his contract, so I fully expect him to be in for pre-season training," said Brown.