The Tigers' £5 million purchase from Fulham during the transfer window picked up the injury on his debut against, former club, West Ham at Upton Park, with some fans fearing he had suffered a recurrence of the injury he sustained at Fulham in September 2006, which kept him out for 16 months.
However, Brown revealed that the midfielder's visit to, American knee specialist, Dr Richard Steadman - who helped nurse Bullard back from his injury at Fulham - was a successful one, with Steadman failing to find any serious problems.
"Hopefully he'll come through a week of training unscathed and we can play him in the Cup against Sheffield United," Brown told BBC Radio Humberside.
"The severity of the old injury sort of plays tricks with your mind and Jimmy would have to be 100% to cross the white line."
Bullard has now joined up with the rest of the squad in Dubai for a some warm-weather training ahead of the club's FA Cup Fifth Round clash against Sheffield United at Bramall Lane on Saturday.
Meanwhile, Hull striker Daniel Cousin has successfully undergone minor knee surgery and is expected to return to first-team action in a couple of weeks.
"I had the same operation about two weeks ago without any kind of rehab," said Brown. "I am running around like a lunatic, so I expect Cousin to be back in about 10 days' time."
